Power Equals Rarity

Let's face it: in Real Life, if a weapon is powerful, it's mass-produced. If an animal is powerful, it flourishes. If a nation is powerful, it can effectively Take Over the World.

That's not the case with games, though. Generally, for balancing purposes, the more powerful an item/mon/etc. is in a game, the harder it is to find. While various reasons are given in the plot (if at all) as to why these things are so rare, in the meta-sense, it's for balance. If the player has unlimited access to game-changing stuff, then the game is tipped entirely in their favor.

This is seen most commonly in Role Playing Games, both tabletop and video, so that the character/party doesn't get so powerful the Big Bad is killed off as fast as a mook, and in collectible games, so that not every player has a game-breaker, and the number of game-breakers out there are limited. Sometimes, the rules of a game specifically will limit an item/mon/card/etc. to only one per player (often retroactively, once it comes to light that the object in question is So Good Its Banned).

Generally speaking, people have come to associate rarity with power, and vice versa. In any collectible game which have common, uncommon, and rare items, it's generally understood that the rarer individuals should be the most powerful; mechanics which would only be okay as a rare are considered incredibly powerful as uncommons, for example. Even in games where the creators actively say that rarity means crap in relevance to power, people will still associate rarity with overall power, even when it isn't. In certain TCG formats, the disproportionate distribution of power between the common and rare cards could lead to Fake Balance.

The basic reasoning for this may come from, of all things, history and mythology, wherein the most powerful items, supposedly-magical or knowingly mundane, were of exceptional quality, but very scarce. This is understandable, though, because the time, resources, and skill needed to create any weapon beyond a sharp stick or axe was great, and an exceptional weapon like Excalibur could, realistically, be made only once in an artisan's lifetime (and was probably the most valuable item in a king's treasury for good reason).

For a video game item (MMO's in particular) that's exceptionally rare and powerful, it has a chance of causing Loot Drama.

Contrast Junk Rare and Promotional Powerless Piece of Garbage for the "rare" and "promo" inversions of this trope. Compare Game Breaker for a retroactive application of this trope, for when something is so broken you might only be able to use one in a deck/army/etc. Often present in games with Level-Locked Loot. Related to Commonplace Rare, when a useful item that by all logic should be easy to get turns out to be extremely difficult.

Literature

 * The Dresden Files justifies this by using explaining that the more people use a certain ritual, the less power one can draw from it. The White Council often publishes texts like the Necronomicon for the sole purpose of robbing them of their power.

Tabletop Games

 * One of the best known offenders of this trope is Yu-Gi-Oh Card Game. Generally, if something's even mildly useful, it's going to be rare or up. The gradations of rarity in Yu-Gi-Oh are many, and the most powerful tend to be the rarest, giving Yu-Gi-Oh the reputation of being a "rich man's game".
 * And sometimes, there were cards that were made useless. Harpy's Feather Duster and Gryphon Wing are a very Egregious example. Harpy's Feather Duster is a pretty nasty card that wipes out your opponent's magic and trap cards. Gryphon Wing, meanwhile, counters it so that whenever they play it, it backfires and wipes out their own cards. Gryphon Wing came in a starter deck, whereas Harpy's Feather Duster usually came with Game Boy Advance game or from a promo... so what was the point of having Gryphon Wing?
 * The Crush Card Virus is almost synonymous within the community for it's rarity and power. It was so rare that in a booster pack with 3 guaranteed ultra rares, it was stated to only occur once in every 10 packs (and rumored to only being printed once every 75 packs). These packs were usually valued at 35 dollars as well, making it quite a stroke of luck to pull one of these. As for power? It could completely destroy your opponent's hand and field of any strong monster, for the next three turns for a comparatively tiny cost.
 * In Dungeons and Dragons, though the rules are set basically by the DM, there are a group of items called "artifacts" which are said to be very, very rare, and literally can warp reality. These are perceived as so rare that they don't have any effective gold piece value listed. In general, too, the more powerful items are limited by DM's so as to make sure the party doesn't go around killing Great Wyrm Red Dragons in a single turn.
 * Supposedly it's this way. In practice, many if not most of the "artifacts" are actually little more than decent but normal magic items with no real special effect. Many others can be replicated with existing spells, and most of those which are really unique are only a little more effective than a "normal" magic item counterpart.
 * In fantasy worlds in general, this trope often applies. This is because, unlike powerful technological weapons, magic weapons often CAN'T be mass produced. They take too much power and energy and effectively have to be hand-crafted.
 * In later versions, artifacts are often times sentient creatures. They have unique abilities when you pick them up, and depending on your characters actions or words the artifact may like you or not. The more it likes you, the more powerful it becomes. If it doesn't like you at all it can effectivly try to sabotage you. Most artifact are designed for temporary uses, as they all have their own agenda and will try to get away from you if you don't seem to at least partly follow their plans.
 * Notably averted in the famous "War of the Lance" campaign for the Dragonlance setting: it is possible for the party to come into possession of four Orbs of Dragonkind over the course of the campaign. Since each one is an incredibly powerful artifact, this has the potential to be a real Monty Haul campaign; on the other hand, they all do the same thing.
 * Magic: The Gathering actively tries to avoid this, at least in some regards. Traditionally, the most powerful cards in the game have not been rares, but uncommons. Still, there are many powerful rare cards as well, which end up being the most expensive cards because of both their use and rarity, and there are quite a few common cards that are considered game-breakers. (This is chiefly because the metagame relies hugely on efficiency, while rares tend to be Awesome but Impractical.) Many feared that, with the introduction of a fourth level of rarity, Mythic Rare, Magic would go the way of Yu-Gi-Oh; these fears, though, have generally been for naught, as many of the Mythic Rares have proven far-and-away worse than most rares and several uncommons.
 * There are still, however, occasional cards that have made some believe that Wizards doesn't avoid this trope as much as they should. The classic example is comparing the mythic rare Baneslayer Angel with the uncommon Serra Angel. Both are from the same set, both cost the same amount of mana, both are even angels, but one is rarer, bigger, has incredibly strong abilities, and is sometimes known as the "Bankslayer" or "BS" Angel.
 * Magic uses rarity to control its Limited formats, where players build a deck from a random or semi-random pool on the spot. As such, spells that require a specialised response tend to be rarer, so players who didn't have access to that special response aren't completely screwed. Many of these spells, though godly in Limited, are poor to useless in Constructed as they cost too much mana. Rarity also controls the complicated-ness of a card: if a card is confusing or just mixes strangely with other cards (but is still awesome enough to keep), it's put into rare so that the problem comes up less often.
 * Most Magic sets are printed on three large sheets that are cut into individual cards: a common, uncommon, and rare sheet respectively. Some sets add a land sheet as a fourth "extremely common" rarity, and recently an ultra-rare sheet is used. There were some oddities in the rarity in the first few sets. The first set (Alpha) had two (normally common) islands on the Rare sheet, and the first few expansions had only two sheets, but had some cards appearing twice or more on their sheet. For example, an U2 card appears twice on the uncommon sheet, and is thus less uncommon than an U1.
 * Hello Jace the Mind Sculptor! It's a Mythic Rare. And so powerful that it was practically compulsory to run multiple copies in any tournament capable deck while it was legal. As a result the price of the card soared.
 * Wizards of the Coast has been pretty good about averting this trope in their miniature games as well. Sure, Rare/Very Rare pieces are going to be the most powerful, but they are not necessarily the most efficient or the most highly sought-after. Discussion threads in both their Star Wars and D&D Minis forums had long lists of competitive armies that could be built using only Common and Uncommon pieces.
 * Averted by sorcery in Exalted. The best known and most frequently summoned demons are those that are the most powerful or useful available.
 * And then played straight by the very nature of reality in every other aspect of Exalted: Humans are common and laughably weak, enlightened Mortals and Godbloods are rarer and stronger, Dragonblooded are more rare and powerful still, while there only 700 Celestials in all of Creation, and they're able to defeat small armies of Dragonbloods. Likewise, powerful Manses, Artifacts, Charms, Sorcery spells, et cetra are all said to be rare and hard to come by (though the design of PCs in any given campaign may or may not support this).
 * In Warhammer Fantasy Roleplay, all magic items are pretty much unique due to time and labour expenditure involved in their creation: Rules for crafting 'generic' magic weapons appears in the Winds of Magic splatbook, where only dwarves can do it and it takes years of off-time to make a single one (and tradition forbids runesmiths from mass producing or making more than one of any particular magic weapon: Only one runesmith ever did it and was stuck with the epithet 'The Mad' for having performed such blasphemy). Even nonmagical weapons and armour tend to be rarer the more powerful they are, but in most cases it's justified by these being cutting-edge and not yet having entered mass production, or simply being unavailable for civilian purchase. Higher-quality versions of regular equipment are also harder to acquire, due to having been hand-crafted.
 * Played with in the Legend of the Five Rings CCG. While it is true that there are powerful rares, several of the most powerful cards in the history of the game actually were only available from starter packs as fixed cards. These generally include the Clan Champion as well as goodies like the Clan Swords. While you could certainly argue cost effectiveness, some of the biggest and baddest characters in the settings have been only available as a fixed card (ie always present in that starter) in their clan's starter packs.

Video Games

 * Pokémon: Mons you find a lot of in one place and/or in many places are weak. Ones which are relatively hard to find, only in a small numbers of places, or you are only given one of are stronger, and ones that you can only catch one of are much stronger.
 * The textbook examples are the Pseudo-Legendary Pokemon, which, as the name suggests, have stats that rival those of Legendaries. They can (most of the time) only be caught in their initial form, in one or two places in the world (and often right before Victory Road), and eat experience like few else. But once they reach their final stage...
 * In Pokémon Black and White, a number of Com Mons can eventually become quite powerful, like Darmanitan, which evolves from a common Pokémon found fairly early on, and Gigalith, the final form to this generation's answer to the ever-present-but-not-nearly-as-awesome Geodude.
 * Then there's the Master Ball, a Pokeball that has an absolute capture rate. It has 100% accuracy and is inescapable once thrown. Typically there is only one of these in the game and is to be saved for the most exclusive 'Mons (like Mewtwo at the end of R/B/Y).
 * World of Warcraft has several Legendary Items, incredibly powerful items beyond the highest Tier, and incredibly difficult to attain (requiring, say, 40 rare drops plus drops from head bosses of the toughest dungeons of the game, or two very rare drops from different bosses plus crafting materials, or just being incredibly rare drops from a specific boss), so there are usually only a few on any given server.
 * Guild Wars averts this, as any Uncommon (read: moddable) can be made functionally identical to a Very Rare or Unique weapon. The real value of the Very Rare and Unique weapons are the skins.
 * City of Heroes has Regular, Uncommon, Rare, and Very Rare Invention recipes. They increase in power with rarity.
 * The Last Remnant features a number of weapons that there are only one of, and are incredibly powerful (most however are found in the course of the main story). Also, the most powerful non-Remnant weapons and accessories require a number of rare components to craft.
 * Borderlands simultaneously plays this trope straight and subverts it: Rare guns are color coded and are supposed to be hard to find, but the way weapon generation works in the game's programming (especially if you are wearing an accessory that increases rare rates,) you'll be throwing away epic loot every fifteen seconds or so.
 * You can not-entirely-infrequently find the second best category of loot in stores. This makes some sense: if every other adventurer out there finds and sells as much blue/purple loot as you do...
 * The effects are much more pronounced in co-op play, possibly to cut down on infighting.
 * The same as above happened in Hellgate London, although this was more of a case of 90% of the gear being worthless to you.
 * Earthbound has one particularly glaring one, the Sword of Kings, the only weapon Poo can use effectively can only be obtained from one enemy, which is only available temporarily, in one dungeon, and it has a drop rate of 1/128.
 * Less notorious but even worse to get is the Gutsy bat. 1/128 droprate dropped by the strongest single enemy in the game, the Bionic Kraken. Also extremely rare, spawns in only one place so you'll probably go through the entire game without seeing one, and so close to the end of the game that all you can use it for is the final boss. It is satisfying to see every other hit be a Smaaaaash! though.
 * Most weapons in the Disgaea series can be of common, rare, or legendary quality (The best weapon of each type is always legendary). The better the quality, the better the item's base stats will be, and the degree to which its stats can be boosted in the Item World will be much higher, as well.
 * Zig-zagged in Dragon Quest IX; just because a piece of equipment is the rarest in the game, it's not always the best. For example, the Infinity+1 Sword you get in the Post Game adds 180 to your attack, while a sword you can get just before the Final Boss can double it. The only reason you'd want to use the Infinity+1 Sword instead of the other one is because it has a surprisingly good chance of decreasing the foe's defense or if your base Attack is less than 180.
 * Like the above, SaGa 2 used this trope, although it also was combined with Too Awesome to Use.
 * Billy vs. SNAKEMAN has this, not at the level of individual pieces of equipment (The way equipment works in the game means that rare gear doesn't have to be any more powerful than common gear to be worth the extra effort), but in the kinds of bonuses that they give. A full set of equipment gives somewhere in the neighborhood of + 40-60 of the inherently diminishing rewards bonuses, but Strength, which can make challenges auto-win in great enough quantities, gets only +16, and Successes, an even more "Game Breaker in excess" bonus, has a mere + 3.
 * One of the draws of Castlevania: Harmony of Despair is collecting rare items. The best stuff is all mostly highly rare item drops from bosses (usually Hard mode only, but some are exclusive to Normal). Other good items drop from purple chests depending on difficulty, some having a tendency to be as rare as the boss-only gear (ie Shanoa's DLC glyphs, the Retro subweapons, and the Fuma gear).
 * Also of note are items that were rare boss-only drops, but became regular enemy drops in the DLC stages. These include Simon's Plate (previously exclusive to Hard mode Dracula, now available from the numerous and much easier Hellmont of Chapter 11), Berserker Mail, and Death's Robe. However, the latter two are still somewhat annoying to get because they drop from mini bosses on Chapter 10, and both are a ways into the level. Still easier than trying to get them from Hard mode Death, as the Chapter 10 versions also drop on Normal.
 * Einhander has the Flash Weapon Pod, a Guide Dang It to obtain normally and can only be obtained twice in an entire game. It's one of the strongest weapons in the game, firing out a pink laser that penetrates enemies and does massive damage in general.

Anime

 * Done deliberately in Shaman King, when Mosuke forges Harusame. The Shogun has him killed in order to prevent him from making another sword, in order to maintain its scarcity value.
 * The Yu-Gi-Oh!! anime takes power card scarcity to extremes. Pegasus kept one copy of Toon World for himself, as he found it too game-breaking to put into circulation, and created only four copies of the strongest normal monster in the game, the Blue Eyes White Dragon. Seto Kaiba, who had three cards, the maximum playable of any card in the game, tore up the fourth one so no one could play it against him, and he would be all but assured to have the strongest deck in existence. And outside of his dragons, Kaiba had even more rare power cards. Of course, all of this precedes the Egyptian god cards.
 * On the other hand, unspeakably broken cards like Mirror Force are found in pretty much everyone's deck, with nearly every character having used it at one time or another.

Real Life

 * This actually comes in to play fairly often with bleeding-edge military technologies, because highly precise, sophisticated equipment often requires manufacturing processes which preclude effective mass production. There were, for instance, only 21 B-2 Stealth Bombers ever produced, each costing over $1.7 billion. They are, however, the most effective low-observability planes currently in existence. The F-22 is going a similar way, with its production currently capped at less than 200 planes, whereas cheaper, less advanced and effective planes such as the F-16 have had production runs of 4500 planes and counting.
 * The economics of war tend to have the standard issue weaponry made to the lowest bidder.
 * As Comrade Stalin says "Quantity has a Quality all its own."
 * Exemplified by the Tiger Tank which when it appeared in 1942 combined heavy armor with long range lethality to become an unstoppable killing machine. However there were only 1,347 examples produced (plus another 492 Tiger IIs) compared with over 50,000 T-34 and 40,000 M4 Sherman tanks.
 * Kevlar is fairly easy to make, but as someone demonstrated on the Discovery channel, heavier weapons (such as a rifle at close range) can pierce the fibers (making it really bullet-resistant rather than bulletproof). In order to really stand up to bullets, needs a Kevlar with ceramic plating woven in, but to do this sort of thing is more expensive, and thus more rare.
 * While stronger life forms tend to out-compete weaker ones within their own species (or niche), small species tend to be more numerous than large ones, and prey tend to be more common than the predators that eat them. This comes down to available energy. A general rule of only 10% of the energy that goes into an organism is transferred to the organism that eats it, the rest is used up by the prey species' own life processes. This limits the amount of energy available to predators thus reducing the possible number of the predator.
 * Indeed all apex predators are always very thin on the ground and thrive when their numbers are such that small prey animals on the scale of mice would be considered on the brink of extinction. Subverted by humans, if only because we're not so picky with our food.