"Make Ursa Major" and "Make Taurus" in Katamari Damacy. Both levels have as their requirement that you pick up exactly one of a given type of item—bear for Ursa Major and cow for Taurus. While any one will do, in order to get the best score possible (and avoid getting mocked by the King), you want the biggest one you can get. The problem is that you're being judged by the original King of All Cosmos... and he is a fricking idiot. He counts statues of bears or cows (and in the latter case, milk cartons) as appropriate items. Nothing is more frustrating than spending five minutes building the Katamari to the right size, rolling towards the giant brown bear... and then bumping a bear cub and getting yanked out of the level. And then insulted by the King.
One of the Taurus start positions put you on the roof of a building. If you roll forward at all, you will bump into a tiny cow-colored pylon and—guess what? IT'S A COOOWWWW! (Level ends).
The cows and bears showed up again in a level in the sequel, We Love Katamari, but this time you had to get one of either. Making it much less frustrating was a new feature added to WLK that let you restart a level if you were unhappy with your results.
What makes it even MORE annoying is that unlike other objects in the relevant stages, the cow and bear items WON'T vanish when they get too small to affect your Katamari's size. This means that it's possible to have an 8M Katamari poke against a tiny windup bear or bottle of milk that is small enough as to be invisible, and have the level instantly end.
For a level from the original that's tough to complete instead of tough to do well on, "Make a Star 4". You have ten minutes to go from five centimeters to one meter. You need all ten minutes.
The North Star in Katamari Damacy has you making a star that is exactly 10m. And you can't easily tell how big the Katamari is. Good luck with that. Thankfully, the King is fairly forgiving.
It helps to look at the size charts before going into this level. Once your Katamari is large enough to roll up a Regular Tree, you'll know you're very close to 10m.
In Beautiful Katamari it gets worse, with the Roller Roaster. Your goal is to roll up hot stuff to hit 10,000 degrees. Problem is, it's far too easy to go careening into big bunches of what the level considers "cold" stuff, and you lose automatically if your katamari "freezes" (0 degrees). And those fire extinguishers... brrrr.
In BK the Roller Roaster level is doubly hard if you're going for 100% Completion, in which case this level has some unique items that you have to be pretty large to get. So you have to balance your temperature with what you pick up and as soon as you get the item you need to make sure you have enough stuff around to finish the stage. Also, the last level where you need to stay away from the black hole until you're large enough to pick it up rather than get sucked into it is like this. Once again, not needed to beat the game but for achievements.
The campfire level from We Love Katamari also appearing in Katamari Forever. You must touch something EVERY FREAKING SECOND or your flame fizzles out in very short order. The objects don't add much fuel to your fire, and if you roll even a LITTLE into the water, you are extinguished immediately. That and Roller Roaster were two levels that a lot of gamers would have preferred to keep in the past.
Not to mention all the OTHER That One Levels that came back... Roller Roaster, the bear/cow level (AGAIN), THREE size challenges, a renamed version of Make a Star 4 that only gives you FIVE minutes... it's like they were trying to create "That One Level: The Game".
WLK is also topped off by a secret level that has no challenge and seems to be there for the sole purpose of throwing off completionists: the rose level. You can leave and re-enter at any time, and the game will remember how many roses you've picked up so far. Each time you enter, the game will provide one of three locales from other levels littered with roses (and bunches of roses, worth 10 each) to be picked up. The roses are all you can pick up, and they don't increase the size of your katamari, which is kind of the point of the game. You need one million roses. It's not for nothing either: finishing the level makes it rain roses on the main map.
Touch My Katamari brings us the diet special. The premise is that you have to roll up as many food items as you can, going up to 30,000 kcal. While that may sound simple, many of the high cal items are placed verrrry close to the low cal ones. There's also a lot of characters who will most likely end up sending you flying in the direction of fatty foods. And, while common sense can mostly dictate what items you should be going for (fish bones, good choice, jumbo burger, bad choice), there are quite a few items that have way more calories than one might expect.
The prison break is infuriating. It's carried out in near-darkness (unless you're in the ghost world, where time stands still) and is both a stealth and escort mission, made doubly annoying due to the fact that it portrays a three-dimensional cutaway of the building in a two-dimensional perspective. It's hard to know, in one area, that you need to have Jowd hide behind the stairs because you can't even tell that area is accessible. If you don't know that Jowd can hide behind the stairs, try figuring out without a guide that Jowd isn't supposed to go up the stairs normally, but has to jump up and go through a grate that one of the guards would be hiding in had you not opened it and made him fall by this point.
Even worse is the heart attack level, notably the one time in the game where you can pass a checkpoint after the situation becomes unwinnable, forcing you to start from the beginning.
The slow-tempo stages of the Lumines series. Depending on how filled with blocks your screen is when you get to them, they can either be these or chances to milk craptons of points. Lumines II is quite nasty with these kinds of levels, putting slow levels right before the last stage of each of the game's Challenge modes. In fact, one stage that was in the original had its line speed halved for II.
Repton is a fairly straightforward game, certainly pretty easy by the standards set by later games in the series, until you reach the eleventh level, "Giant clam". On this level you have to collect diamonds while being pursued simultaneously by three monsters; their unpredictable movement means that often when you turn a corner to get away from one, the others will now be ahead of you. There are no rocks provided to kill the monsters, and every diamond in the field must be taken before leaving that area. Oh, and when you exit the area, a rock blocks it off, so the lower area must then be completed without losing a life.
There is a trick to make this level much easier. It won't help you with the lower area, and costs you one life, but it makes the upper area much, much easier. When the level starts, run immediately to the lower area entrance. When you finish it, make sure the three monsters are stuck right behind that boulder. Take the last diamond and lose one life. The monsters are now stuck and you can pick up all the remaining diamonds without too much hassle.
Tetris: The Grand Master 3 brings us Sakura mode, which has stages that can become nearly Unwinnable as a result of a single misplaced piece. Of note are the following stages:
Stage 8 — Two horizontal U-shaped structures that have gems on their longer sides. In addition to that, the X-Ray item, which renders the playfield invisible save for a line that sweeps horizontally across the field activating every other piece.
Stage 15 — A tall structure shaped somewhat like an hourglass. Unless you make some creative piece placements, you may find yourself needing to do the annoying "soft-drop the piece carefully then wait until it's at the right height" technique to slip pieces into the two overhangs. One mistake in placing pieces in those overhangs and you may as well skip to the next stage.
Stage 16 — The stage itself isn't hard. The killer here is the Roll Roll item, which actives every third piece and causes your current piece to rotate automatically every split second. If you just rush through this stage, you'll have misrotated pieces foiling your run.
Tetris Worlds has "hotline", where only lines at certain altitudes matter.
Several of the gimmick levels for the Jewel Quest games can arguably be this, but there is no denying the monkey challenges. Here, not only do you have to turn all of the squares on the board gold, but you also have to put monkey relics in all of the available cages. The catch? Match up any three or more monkey relics, and whatever gold spaces they occupy are turned back to brown (meaning you'll have to turn them back, again), and they can be matched up with monkeys already in the cages, undoing all your hard work.
Level 8-2 from Zuma is the third version of the Altar of Tlaloc map, which wasn't too bad before, except now you're working with all six colors and a longer starting chain on a map with a laughably short marble track (about 25% of which can't be hit because it's Fake Difficulty under the playfield.) Players have entered the stage with a full set of extra frogs and lost every single one.
The N game has several of these. You play as a ninja who has to collect a blue block to switch open the exit door. Simple right? Now try doing that while avoiding the missiles, electric robots that follow you, the lasers, and the mines. Oh, and you blow up and die if you run out of time. Considering the fact that there are at least 500 levels in this game, there's no doubt that at least ten of them will piss you off to no end.
In the Katamari Damacy clone The Wonderful End Of The World, the Cafe Internets level is significantly harder to get a successful score than any other level in the game. It's easy to become just large enough to make navigating the level practically impossible.
Tetrisphere's Hide n' Seek mode has any level with the rare Crystal Tower rules. Tower rules task you with destroying\moving all the blocks around a tower to expose the picture underneath. Crystal Tower is much the same, except now the tower breaks if you move a block into it, or if any block is destroyed nearby. Normally you have 3 lives but breaking the tower is an automatic loss.
While a breather after the Crystal Tower before it, the last Hide n' Seek level is the only level that starts with a donut with the blocks stacked all the way to the top. This means the entire thing glows red when you start, and you need to move blocks into crystals just to free some space to drop blocks into.
In the online game Psychopath it's Level 55, Spaceship. The object of this game is to reach an exit in the given number of moves, which will always be the fewest possible. Spaceship tortures the player with a dozen possible approaches that fall just short, making it very hard to choose the correct approach. Even the level's creator originally set it to 221 moves — then someone else pointed out that it can be done in 219, so now, of course, that's required.
Another notable level is the aptly named "Totally Unfair". Earlier you did a level named "Totally Fair", in which you had to lure a teeth (which will always move 1 square towards you if they can) through a maze and onto a brown button. It was actually a pretty easy level. Then later on comes Totally Unfair, which is the exact same level, with 2 distinct differences: 1. You cannot see the teeth or the maze the teeth has to move through. 2. You have only 60 seconds to complete the level this time around. How on earth are you supposed to beat this level when you can't even see the maze or the teeth? By memorizing the EXACT pattern of the maze and the movements the teeth have to make to get through it, and timing your movement accordingly outside of the maze so that the teeth will still attempt to chase you through it, even though you're multiple screens away. Did I mention there are bear traps all over the maze? If you make any type of mistake, including not timing said movements EXACTLY right, the teeth will be stuck, and you'll have to restart.
The dice puzzle in Virtue's Last Reward. Fairly straightforward yet annoying in the Archives, and very hard in the Q room. There, it's not enough to have the dice in the right positions, they also have to be oriented properly as shown on the illustrations, which requires a certain amount of moves for each of the dice.
Opening the pod room door in the Treatment Center requires you to play a game of Mastermind, except you only get ten chances to guess the password and it's randomized after those ten attempts. Mitigated slightly by the fact that numbers aren't repeated, but it's frustrating all the same.
The Pressure Exchange Chamber after Clover basically says Screw This, I'm Outta Here! and leaves you and Tenmyouji stranded in the chamber, because what you have to do and how you have to do it to get out isn't very clear. Also the puzzle on the door to get in and out of it requires a very steady hand in order to connect the dots, and the touch screen can be rather finicky. Even better? The game likes to crash randomly upon starting the puzzle. The PEC Room in general is pretty buggy.
Angry Birds: Any level requiring precise timing or aiming can turn into this. Especially in the "Friends" version, where you want to score higher than your friends. Sometimes,killing the pigs is easy, but taking out enough debris with them to get a top score is hard. Plus, some levels in that version work best on Facebook, leaving mobile players wanting to hurl their phone/tablet across the room. Oh yeah, and the aimer in most versions is a powerup in "Friends", rather than a standard feature. It also doesn't help that there are projectiles flying at the birds in some levels of most games. And yeah, you can use powerups but even if you have money/game coins to buy them, they lower your score.