Unbreakable Weapons

In a bizarre dichotomy, if video games don't have Breakable Weapons, they very likely have the exact opposite: Unbreakable Weapons. No matter how many times you rapidly fire that gun in full-auto mode, it never malfunctions nor does it ever require any sort of maintenance. Swords never break no matter how many times you foolishly use it to strike armored enemies. Unless, of course, the plot calls for it.

Action Adventure Games

 * Every The Legend of Zelda game. Ocarina of Time had the breakable Giant's Knife, and wooden shields can be incinerated in all of the 3D games, but this trope applies to almost all the standard items and equipment in the games. A certain enemy throughout the series can often eat your shields, but that's not exactly breaking them. In fact, in later games they'll drop them intact if they're defeated quickly enough.
 * Mark of Kri and Rise of the Kasai play this straight. You can bash your sword against armor, other swords, and stone walls-- you can block a heavy axe swung by a Mighty Glacier with a pair of knives, but your weapons will never break. Not even the wooden ones.
 * Most of the games in the Legacy of Kain series play this straight; in Blood Omen, none of the weapons can be broken. In the Soul Reaver games(I could be wrong on this one) none of the weapons you pick up-- many of which are ceremonial or even decorative-- will break, though you'll lose them. Defiance also features an unbreakble sword in the form of Kain's Reaver. Blood Omen 2 is the only game to feature breakable weapons, and even then, they're only breakable when you're using them; enemies can block your(superhumanly strong) attacks infinitely without them breaking. However, even this game features an unbreakable weapon in the form of the Soul Reaver itself, which is obtained in the last bossfight or by a cheat code. Being unbreakable is a plot point for the Soul Reaver, however, it's also the only weapon that is broken as part of the plot, whenever it strikes itself(time travel), one version will break.
 * While armor can degrade in Assassin's Creed II, none of Ezio's weapons ever break. It is somewhat justified in the case of the iconic Hidden Blade, whose construction is far ahead of its time.

Beat'Em Up

 * The Double Dragon series is notable for being one of the few beat-'em-up franchises to feature unbreakable weapons. Specifically, melee weapons such as the baseball bat and the whip or large objects like oildrums or boulders, can be wielded by the player as much as possible, provided the player doesn't lose his weapon by having it fall off-screen out of his reach or into a pitfall. However, the player will drop any weapon his character is wielding after reaching a certain point (normally after completing a stage). In the NES games, weapons will vanish when their original wielders are killed.
 * In River City Ransom, anything that can be used as a weapon can be picked up by the player and used indefinitely as long as it's on the player's possession.

First-Person Shooter

 * Every Halo game. Guns never jam, although alien weapons normally overheat from uninterrupted continuous fire, and/or run out of energy and must be discarded, except for certain weapons.
 * I'd say it extends to practically every shooter in existence. Gears of War may be an exception... but it only jams when you manually click the reload button at the wrong time while reloading. Not clicking the button means it takes a bit of time to reload... but removes the risk of jamming the gun.
 * However, there is a good reason for this. Players never go to the toilet or get sleepy either in those games.
 * Special honors ought to go to Gordon Freeman's guns in Half-Life. Any weapon that can still happily fire at full auto despite being immersed in water, toxic waste, massively radioactive liquid that damages the HEV suit, fire, and cold intense enough to cause death in less than a minute deserves the unbreakable title.
 * And even more special honors go to Gordon's iconic crowbar, which suffers not a scratch or dent from all of the above and being used to smash things for almost the entire game.
 * For that matter, pick any Half-Life mod or Source based game.
 * All weapons in Bio Shock are unbreakable, even the ones that are made out of spare parts

Hack and Slash

 * Drakengard's weapons are Unbreakable Weapons. Kind of funny in that some of the weapons themselves are broken, but won't break further.
 * Devil May Cry deserves special mention, considering some of the downright ridiculous things that Dante does with his sword, such as jamming it into the ground and using it to spin around repeatedly, continuously twisting the sword through a foot of solid concrete. However, since it was said before that Dante fires bullets from guns using his demon energy, and pretty much all of his weapons are demonic in nature, this may not be too much of a stretch by some.
 * The original Diablo had a durability exploit in which, through the use of Hidden Shrines, can raise the durability of an item to the specific value of 255, which the game recognizes as indestructible.
 * The sequel provides intentional examples, such as mods and socketables making an item indestructible.

MMORPGs

 * Runescape weaponry is unusually resilient, for example an axe will continue to fell trees after breaking a thousand steel platebodies to bits. Barrows Armor, however, is extremely old (thousands of years) and will break and decay after fifteen hours of solid use, until it needs to be repaired for hundreds of thousands of coins.

Role Playing Games

 * Every Final Fantasy game. Hell, just about every electronic RPG ever made. Swords never break, and guns never jam. The maintenance portion can be handwaved in most games and RPGs by saying they sharpen blades and maintain and oil guns during down time between battles off screen.
 * Early games had archery consume arrows, which is a partial aversion.
 * Weapons (and armour) in Final Fantasy Tactics can be broken with Knight or Divine Knight skills, Samurai abilities in the same game could break the katana it used, and there was the Ogre Nix in Final Fantasy VI which would randomly break after use. But this can be prevented with the right Support ability.
 * Irvine from Final Fantasy VIII actually had limited ammo for his guns... though only in his Limit Break.
 * Of course, Final Fantasy VIII actually said that weapons were completely indestructible as part of the SeeD ranking exam.
 * One common exception is items that can be used to invoke some kind of magical property, generally casting a spell for no MP cost. Even when the item could be used to strike enemies forever without a dent, one use of its mystic power is likely to shatter it forever.
 * Even this isn't consistently the case, as in the first Final Fantasy, III and IV, spell casting weapons never break after use. As a tradeoff, they are generally limited to casting lower level spells.
 * In the original Baldurs Gate any non-magical weapon can break after a random period of use. This is attributed to weakness happening because and not due to a natural property of iron, though. It also stops happening after.
 * Every Seiken Densetsu game. Unlike the previous two examples, there are no exceptions to this. The Mana Sword does seem to rust easily, but it never breaks.
 * Valkyrie Profile has both Breakable and Unbreakable Weapons. The breakable variety are said to have been made by humans or are barely able to contain the vast amount of power they hold, while the unbreakable ones are made by the gods and have an "ether coating" rendering them indestructible.
 * Silmeria does this unless a specific Sealstone is used, and Covenant is like this regardless... which is confusing, since both are prequels.
 * Star Wars: Knights of the Old Republic. Most physical melee weapons are coated in a supposedly-rare Unobtainium to keep enemy lightsabers from cutting through them like butter. Firearms of all sorts have infinite amounts of the appropriate ammo. Lightsabers... are about as indestructible as you'd expect. They're still Game Breakers.
 * Lampshaded in KOTOR 2, when you meet a Mandalorian who had his spare ammo eaten, his gun's ammo depleted, then broke the gun by using it as a club. He points out that he was careless because, hey, when was the last time YOU ran out of ammo?
 * Most of the Ultima games feature this. Exceptions are usually magic weapons that can run out of charges. Ultima Underworld subverts the trope, with only the Infinity+1 Sword being this.
 * Golden Sun averts this. Items/weapons that can be used as items, if used in battle, can and frequently do break. You can get them fixed, but not mid-battle.

Third-Person Shooter

 * The Crusader games' weapons are Unbreakable. This is odd, because the RP-22 and RP-32 are explicitly described as "indestructible" due to their construction, but no other weapons are.

Turn Based Strategy

 * Fire Emblem usually has one or two unbreakable artifact weapons per game, as an exception to otherwise being a superlative example of Breakable Weapons.
 * 1, 3 and 11 (all remakes of eachother for the most part) have an item that makes any weapon held by the character wielding it unbreakable.
 * Near the end of Radiant Dawn, you get to make any weapon you want unbreakable for the rest of the game, so long as a character sent into the final campaign can use that weapon. This includes long-range tomes that normally have only five uses are so.

Non-Video Game Examples

 * Captain America's shield is completely unbreakable. The few times it's been broken were either retconned away as weaker copies or the villain had reality-warping powers and due to the natures of the stories, the shield was restored in the end.
 * In a cinematic GURPS game guns never jam, swords never dull, knives never break and so on. Interestingly this has no effect on shields, the default assumption is that shields cannot be broken by any force.
 * A literary example would be the Redwall series, where Martin The Warrior's Thunderbolt Iron sword has lasted for possibly centuries (including a lengthy sojourn on the roof of Redwall Abbey, exposed to the weather for many seasons) without ever rusting or losing its edge.
 * (Although it starts off "broken" by Martin's archenemy, and only gets Indestructible after a Badger Lord re-forges it.)
 * Samurai Jack and his buddy/rival Scotsman have magic enhanced/blessed swords that are designed to be freaking tough.
 * The Legendary Weapons in Kyoryu Sentai Zyuranger. The Zyurangers sought them after Dora Skeleton sundered their original weapons with no effort whatsoever.