Secret Level

Many games provide secret levels that aren't necessary to finish the game. Sometimes they are based around gimmicks or themes that aren't in the "actual" game. Sometimes they are much more difficult than the main game's and are essentially a secret challenge, or they feel like they could fit right in the game and were seemingly left out of the main game simply because there was no way to fit them into the progression (and making them secret was better than leaving them out or dummying them). Naturally these will be necessary for One Hundred Percent Completion.

Then you get games that have "secret levels" as a major aspect of their design and designed in from the start as a major part of the overall design (generally games heavily based around 100% Completion).

Action Adventure

 * In Zelda II: The Adventure of Link, you can go to Darunia and climb on top of houses. If you go to a roof nearest the top of the screen, you can jump off-screen with the JUMP spell, then (while still off-screen) use the FAIRY spell and fly up. You'll get the animation for falling down a hole and end up in a DIFFERENT town. The villagers all provide game info not found anywhere else in the normal towns. If you exit under the overpass to the right, you'll end up in the middle of the ocean, not being able to move in any direction. If you exit to the left, you'll just end up outside Darunia.
 * Tomb Raider 3 has a secret level accessed by finding every (well, technically, all but one, due to an oversight) secret. It appears to have been intended to be a normal level (and showed up in various previews of the game) at first but was cut for some sort of progression reason.
 * The Tomb Raider 2 Gaiden Game Golden mask also has a (very wacky) secret level accessed by finding all the secrets in the previous levels.
 * Tomb Raider: Anniversary has the "style units" gained after finding most of the secrets. Not really a level as it is just an explorable visual demonstration, but it shows off various experimentations with the art-style of the game and locations.

First-Person Shooter

 * Pretty much every early 2.5D FPS (and 3D, with Quake) has a secret level at some point or other, whether it's once an episode or just one or two in the whole game. They are usually accessed by using a hidden, secret exit on a level rather than the regular exit.
 * Doom II had two secret levels set in levels taken from Wolfenstein 3D, with one accessed from a secret exit found in the other. The second one required you to kill four clones to access the exit.
 * Descent had some secret levels late in the game. They were difficult, but you could be rewarded with a lot of points and some weapons upgrades.
 * Quake 2 had three secret levels. The first - Lost Station - has noticeably more enemies than usual but doing it will reward the player with an early Super Shotgun. The second - Sudden Death - is an interesting one: upon entering, you have 30 seconds to grab as much stuff as you can then you're thrown back to the previous level and can't enter again. Oh, and it's entrance is an innocuous waterfall in plain sight but can only accessed via a Rocket Jump. The third - Comm Satellite - is set on a space station accessible via a hidden teleporter and as such, has low gravity and only flying enemies.
 * The Aztec and Egyptian levels in Golden Eye 1997. The former deals with the Drax Corporation from Moonraker, and the latter has Baron Samedi, who somehow procured the Golden Gun and is taunting MI 6 with it (that level doesn't make a whole lot of sense story-wise, come to think about it). The levels carry their own unique challanges: the Drax soldiers have an over-reliance on grenades which sharp-shooting players can turn against them, and the Egyptian tomb has a Guide Dang It method of getting the Golden Gun.
 * The "Panzerknacker Unleashed" missions in Medal of Honor Underground. They are based on multiplayer maps from the previous game, and they are very, very hard.
 * Level 4-0 in Medal of Honor: Allied Assault is accessible only through the console, and looks like it was supposed to be part of Mission 3, but was Dummied Out for progression/pacing reasons. There's also the Bazooka-Med bonus level accessed by earning the medal on Sniper's Last Stand.

Hack and Slash

 * The secret Cow Level in Diablo 2, which was made after various rumours about one in the original Diablo.
 * Diablo III has Whimsyshire, a land that seems ripped straight from Care Bears with smiling clouds, purple bears and unicorns.

Platform Game

 * Ratchet and Clank (in 2, 3 and A Crack in Time) has the Insomniac Museum, where the game's designers stuck a bunch of stuff that "didn't quite make it into the finished game." The handheld entries have the High Impact Games Treehouse, with much the same purpose.
 * Commander Keen Episode I had a secret level which could only be accessed by going down a tricky side passage in another level.
 * Episode four had one where you collect 12 Inch Worms to make a giant foot which then launches you to a secret temple.
 * Sonic CD has the Dummied Out 8th Special Stage. To access it, the player has to enter a code in the title screen to open the secret Sound Test, then enter another code on it.

Real Time Strategy

 * StarCraft: Brood Wars featured a secret mission which hinted at a major plot point in the sequel. It had no lasting impact on the game otherwise. Said sequel also features a hidden mission in the Terran campaign.
 * Similarly, Warcraft 3: The Frozen Throne had a hidden tower defense mini-game. If you defeated all the waves, you would receive a bonus hero in the following level.

Role-Playing Game

 * Quest 64 has a Secret Level in the desert. While in a completely unrelated and skippable area, it does have a ton of powerups which are normally hard to find.
 * Dark Souls has The Painted World of Ariamas, the Great Hollow, and the Ash Lake. For the most part, they're difficult to find Breather Levels with lots of really good loot.

Shoot'Em Up

 * The Sharp X68000 port of Fantasy Zone has a secret eighth stage, "Dragon Land," based on Space Harrier.
 * Rez has the Lost Area, unlocked by completing all the normal areas. It is quite difficult. Same for Child of Eden's Hope level.

Action Adventure

 * Bubble Bobble, NES (and thus Virtual Console) version has a secret path that the players must take to get the best ending. It wasn't there in the arcades.

Action Game

 * Rolling Thunder 3 for the Genesis has Rounds A-C (one of them being a Nostalgia Level) that serves to substitute the two vehicle stages (Round 3 and 6), as well as the Hijack stage (Round 9) while keeping all of their current weapons and ammo.

First-Person Shooter

 * The secret levels in Perfect Dark are markedly different from those in Goldeneye mentioned above. Instead of brand new levels with no plot significance, they're retreads of previous levels from a different point of view, which reveal different parts of the story. The first one shows how an alien Mook . The other two missions let you play as the grey aliens, one where Elvis alerts the Institute of being captured by Area51 and you play through the entire level with diminished health, and the other has you play as a soldier among a platoon who landed on the planet after Joanna dropped the shields. Both missions are insanely difficult.
 * Marathon Infinity: Blood Tides of Lh'owon has several of theses, which are either alternate endings where the W'rkncacnter destroy the universe, or "co-op carnage break" levels that can (or are supposed to) only be accessed in multiplayer mode. Then there's the three Vidmaster's Challenge levels, found via a secret exit on the final stage. Taken to impossible levels with "Hats off to Eight Nineteen," a map that can be compiled using hexadecimal code present in game.
 * Nitemare 3D goes straight from level 4 to level 6 if you play it normally. Or, you can simply push a bunch of boxes in front of one of a pair of dumbwaiters (which will otherwise just transport you back and forth) and get in the other to jump to level 5, which is full of gun-wielding human enemies.

Platform Game

 * Wario Land, almost every game in the series has many secret levels, including whole secret worlds.
 * Super Mario World also has many, many secret levels and two entire secret worlds.
 * Super Mario 64 has various secret levels hidden in the hub area.
 * Super Mario World 2 (Yoshi's Island) had one secret level per world (accessed by 100% completion of the normal levels), generally based around a gimmick, much harder than other levels, or both. The Game Boy Advance remake has another secret level per world once the game has been beaten.
 * New Super Mario Bros. has secret exits that have red flags instead of the standard black flags. Some let you skip sizable chunks of the game.
 * Worlds 4 and 7 are also secret worlds.
 * Luigi's Mansion has multiple hidden, secret or otherwise unneeded rooms inside the game, which are essential for 100% completion and getting all of the ghosts, but is often entirely optional and one may even forget to do them while playing because those rooms are never mentioned.
 * Super Mario Bros.: The Lost Levels has World 9, which the player could access only by playing the first eight worlds without warping.
 * And Worlds A through D, which in the original FDS version the player accessed by playing through the main game eight times. In the All Stars version, you go straight to them after World 8 or 9.
 * Super Mario Land 2: 6 Golden Coins has two secret levels in the Pumpkin Zone, and one each in the Tree Zone, Macro Zone, Space Zone and Turtle Zone.
 * Two words: Hungry Lumas.
 * Donkey Kong Country 2 and 3 have a "secret" world, that allows access to a better ending and certain items you collect are focused around gaining access to these levels.
 * Crash Bandicoot has several of these:
 * The first game contained to two levels that you needed you to get keys from the Cortex Bonus stages.
 * Crash 2 has levels hidden within levels. Some of these are considered parts of the main level where you really need to know what you're doing to find them...
 * ... For instance there's the hidden area within the Unbearable level where you need to jump into a seemingly bottomless pit in order to gain access to a hidden area within the level, which swaps the level theme from a towards the screen chase sequence, to a side scrolling section.
 * ...On another level, the player has to jump on what looks like a conspicuously static stack of Nitro crates to teleport to a secret section and get the purple gem.
 * ... Then there are the levels which you need to unlock by finding secret bonuses in other levels, such as standing on a hard to get to platform, or jumping over a long hole, to get back to the polar bear, in order to unlock hidden levels, and alternate paths in other levels.
 * Crash 3 does the same once again in accessing hidden levels with alternate routes, but makes you beat time trials to get to them. However, there are still two hidden levels not at all required for 100% completion, but required for the 105% completion. While all of the secret levels in Crash 2 can be found without a guide with enough persistence, Crash 3's secret levels are really obscure. One of them has you driving into a sign on the side of the road in a motorcycle level.
 * Sonic and Knuckles had both secret areas that were only accessible by one of the characters, and a different final stage for 100% Completion.
 * Iji has Deep Sector, featuring a fun little battle against seven Assassins. Considering the most you ever have to deal with at one time other than that is one....
 * Eversion's secret level is unlocked after collecting all 240 gems in the game, and is necessary to get the good ending.
 * Demons Crest really has no mandatory levels after the very first stage, but the final two need to be unlocked on the world map by jumping into a cyclone in Stage 4.
 * Super Meat Boy has regular secret levels which qualify as bonuses (required for 100% Completion), and then has intentional "Minus World" levels, which are just plain sadistic.
 * In Mega Man X3, there's a secret level that can only be accessed through specific teleportation capsules, that take you to an abandoned factory where you can fight Vile, The Dragon of the first game. Finding and beating him will result in another boss appearing in his stead later on, where he would normally find and attack you.
 * Then, in Megaman X6, there 's a secret "Nightmare Stage" for every normal level, where you can find secret upgrades and bosses.

Shoot'Em Up

 * Tyrian is absolutely chock-full of secret levels. As a rule, they're accessed by destroying a specific target in a level so that a big glowy sphere appears. When you grab it, you'll move on to the corresponding secret level after finishing the current one. Some of these are tough to get, requiring you to leave certain enemies alone or stay on a certain path. There's even secrets 'within' secret levels, so you can go through a bunch of secret levels in a row before returning to the normal ones.