In the original version of Space Quest I, you have to escape the Arcada before it explodes. Yet you are not explained ANYTHING about this other than "the Arcada was boarded by unknown assailants".
Actually the game leaves it up to you to find this out. You can go to the main bridge, which is actually not too far away from the starting point, and read the console. It will say the ship is set to self destruct and has a time counting down. But you also don't have to enter the bridge at all to continue and you could easily bypass it completely without realizing it was even an option, and the timer is pretty lenient. The VGA remake displays a clear timer.
In Space Quest II, there was a maze that was a non-cursor version of a pixel hunt. If you touched the (pixel thick) walls with your (pixel sized) foot, that's it. Boom, dead, game over. Back in the day of playing on 512k floppies, this maze represented one of the most tedious things in the world. The maze isn't difficult - you can see the whole thing from the outside the whole time - but navigating it is incredibly tedious and frustrating. And then, having achieved all this herculean task... you have to do it all over again. Backwards.
And for those of you who actually have feelings for Roger, the death described by the game during that area is probably the worst death possible for Roger (And given the myriad of deaths he could have, that is saying a lot.)
And speaking of Space Quest, a number of arcade sequences in the series are rather hair-pulling, even by adventure game standards:
The Zero-Gravity Skating sequence in Space Quest IV... even on a system slow enough to work at the right speed, it's still damn near impossible.
Rescuing Cliffy in Space Quest V... really a Luck-Based Mission, but the odds of your fuel running out are really really against you.
Curse you, Astro-Chicken. You are the one thing standing in the way of Space Quest III being the best of the series. Sure, it's not required to beat the game, but anybody who cares about the plot enough wouldn't allow themselves to search for the Two Guys without playing it first. Otherwise, why are you even going to Pestulon in the first place?
The stupid cliff climbing section in Kings Quest III — you have to inch Gwydion down a cliff with no indication as to which pixels are the very, very small minority which will not send you plummeting to your death.
Want to go up or down stairs in upper levels of the Big Bad's castle? The stairs are on the near wall, so you can't see how the steps curve or how wide they are, and if you fall off, it's game over. Have fun!
The desert in Kings Quest V. Finding the oases and the bandit camp (and a certain item that you need to complete the game lest it becomes Unwinnable) is trial-and-error, unless you have a map. And even after getting past that one, there's the catacombs of Mordack's dungeon late in the game, with a very confusing map system.
The Catacombs in KQ6 aren't nearly as bad as anything in KQ5. Although the falling thing is cruel, an observant player will notice that the floor disappeared where in the instead-death chambers it's gone from the start. Getting stuck because of a missing item is annoying, but because the catacombs are self-contained you don't have to go back too far (unlike in KQ2 where you can end up having to replay half the game if you crossed the bridge once too often). And unlike with the KQ5 Yeti custard pie example, you can actually figure out what you're missing ( if you get stuck in the dark, obviously you need the tinderbox from the pawn shop; and although the brick and the red scarf are slightly less obvious, you can make the connection once you find those items if you've been in the catacombs before).
Microscope Puzzle in The Seventh Guest. Probably 90% of the people who will tell you that they didn't have to skip this puzzle with the hint book are filthy liars. And for good reason.
Unfortunately, the AI isn't random in the least—if you do the exact same movements every time, the computer will do the same moves every time, depending on your PC specifications. Even attempting to mimic a YouTube solution video will cause you to lose if your PC is faster or slower.
Fortunately, most people that play DOS-Era games today do so with DOSBox, which allows you to specify a CPU speed. How people did it on the old machines is probably a bigger guide-dang-it than the puzzle itself.
Any of the bike fights in Full Throttle. They weren't well programmed to begin with, but they're actually unwinnable using ScummVM if you don't just cheat and use the instant win code.
Made worse by the fact that the instant win code, in DOS, had this knack for NOT WORKING PROPERLY and screwing you out of an item. oh, and there's only 3 of one specific type of enemy which holds an item required to progress, and if you used the cheat, you'd not only fail to get the item but be unable to cross a destroyed bridge.
Also the segment where you have to kick the wall to sneak into the Corley Motors factory. There is literally no indication of where to kick beyond an extremely vague clue that the kicking spot would have been short enough to be reached by a child. So, good luck pixel hunting!
HINT: You don't have to wait until the meters go black to test the spot. The spot will make a different sound when kicking it even if the meters aren't black.
Torin's Passage had the Slippery Slope: a steep slope with few viable handholds, which were totally invisible and only detectable when you moused over it and the talking grass gave an affirmative. A variant of the Pixel Hunt.
Runaway: A Road Adventure. Chapter One, Scene One. "Hmm, I should write over this board so that the killer after Gina mistakes her for someone else and leaves. Hey, I have a marker, but it's dry ! Hey, I have some alcohol ! But I'd need something pointy to refill it... a pointy container... in a hospital..." Well, good luck finding the 2-pixel-wide zone holding the freaking syringe now. Perfectly logical and sensible puzzle killed by Pixel Hunt again.
7 Days a Skeptic of the Chzo Mythos games was particularly painful when the player was being chased about the space station and died if the enemy got within a few pixels of him (in a small windowed game). While the chasing was not TOO bad if you played things safe, the worst parts were the puzzles to defeat said assailant, usually involving doing things that were much more elaborate than would realistically be necessary.
Oh, come on; during the chase he can pop out of any door in the ship. Including a locked door. A locked door that you had to stand next to and unlock manually. While it was still locked.
Zack & Wiki: Quest for Barbaros' Treasure: Barbosa's Island starts by making you pull a trap door that will kill you unless you grab a grate in a split-second (after getting the pointer on screen which was hidden during the previous sequence of course), and goes downhill from there. Especially frustrating is fighting the skeletons with a sword, and the controls are terrible. And the level ends with a minigame where you need to pull a rope just before Barbaros reaches you ... and yes, failing this minigame does count as death.
There's also the Frost Breath level, which is a very frustrating mirror puzzle where three incorrect fires of the cannon result in losing a life, or the Dragon Scales level, a long and intricate level with a lot of steps that requires a LOT of forethought or else the player renders the level Unwinnable.
Meh, I didn't really mind Frost Breath. However I feel Dragon Scales needs to be expanded on. What you said doesn't even begin to describe how easy it is to make it unwinnable. To complete it, you must climb into the dragon statue at the start, pull the lever inside the head twice, (once to drop the bridge into place, the second to move the statue's claw into place,) cross the bridge and remove the claw from the dragon statue, put it into the flamethrower statue at the centre, use it to kill the two spiders on the other side, turn the sleeping pirate and one of the aforementioned spiders into a totem and tennis racket respectively, stand on a certain podium, use the tennis racket to hit one of the statue's fireballs back to hit a third spider, (a challenge in itself, and you lose points for every miss,) and turn another sleeping piate into a second totem, before rolling one of these totems and the bridge down a ramp to form a see-saw at the bottom, put the other totem on the see-saw and jump on the other end to throw it across. Take a spider-racket, set the fire statue to push a nearby boulder onto one end of your see-saw while you go on the other end, then plug the nearby lava-drain thing with the totem when you're flung over, hop on the other podium, hit a fireball across with your racket to free the treasure chest and have it land on the see-saw, dislodge a second boulder to have the chest flung to you. Sound difficult and intricate already? Well, if you are to mistime just one step here, you will be unable to finish the stage. ...Yeah.
The parlor in Dream Chronicles, where you have to find seven pictures, some of which are ridiculously well-hidden. Then you have to put each of them in the correct spot on the wall, causing the piano to play a melody of varying length, during which you can't do anything. THEN you have to click on each picture and play back the melody on the piano. Oh, and did I mention that after you successfully play back the melody, it plays it back AGAIN and you can't do anything?
Yume Nikki has the "Hell" maze. Not only does it glow red, giving it a very unsettling look and feel, it's also the largest area in the game, is extremely difficult to navigate, and there's a toriningen or two to avoid. But navigation of it is necessary to obtain a few effects.
The teleport maze. Without a map, you will get lost.
The stone room puzzle in Riven is one of the hardest puzzles in the game. You have to deduce the order in which to choose five symbols (from about thirty in total). This is accomplished by 1. learning the D'ni numbers in the school; 2. noticing the five wooden spheres on the island with the village (note: one isn't reachable in its proper location and can only be found in a completely unrelated place); 3a. notice the sound they make (one of them doesn't make a sound however) and find the relevant animals or 3b. notice that when observed from a certain angle, they form the "eye" in the symbol you're looking for (one of them doesn't have this, though). Although most players will get the sound-based clues, the shapes are hard to notice so if you didn't, tough luck solving the one that doesn't make a sound, especially since that's the one you can't reach so its shape can only be observed through a telescope viewer in yet another unrelated location (and you can't really see the sphere through the telescope either). I've yet to hear of anyone who noticed that shape without hints; those who solved the puzzle without hints either just tried all symbols for the missing sphere, or reasoned that since the sphere was in the water, it should be a fish.
In Indiana Jones and the Fate of Atlantis, you have to navigate the submarine and enter a cave. Sounds easy? Think again. In order to properly align the sub in the cave, you have to navigate in 3D while your view of the screen remain in 2D.
Strong Bad's Cool Game for Attractive People has a few toughies. There's the Maps and Minions minigame at the end of Strong Badia the Free, and the final puzzle of Baddest of the Bands, where you have to mess around with both the stage fixtures and Strong Bad's bandmates in order to reveal Strong Bad's much-vaunted "ultimate stage prop".
In Sam and Max Hit the Road, there's a magnifying glass hidden very well in one of the tents at the carnival, it's hidden so well that you will mistake it as part of the background. Then when you have all of the equipment to modify the binoculars at the World's Largest Ball of Twine except for the magnifying glass, and try everything in your inventory, you will no doubt rage.
The Walking Dead: Episode 2 has one. Near the end, when Brenda is holding Katjaa hostage, you have to advance on her very slowly and stop immediately when she points her gun at you, then talk to her. However, you must stop on a dime when she does, or she shoots you on the spot. And you have to do this THREE TIMES.
Anyone who has ever played Amnesia The Dark Descent remembers and utterly loathes the Cellar Archives (also known as the Water Part). Not because it's a particularly difficult puzzle compared to others in the game (though it's certainly not easy), but because it's INSANELY, PANTS-CRAPPINGLY TERRIFYING. In a game known for possibly being the most terrifying ever made, this section is the one most often singled out for being the scariest part.
Ditto for the Dungeon level in the free expansion pack, Justine, which also happens to be filled with water. This part is often regarded as one of the scariest chase sequences in the entire game, since you have to rush through the item puzzles as fast as possible to get away from the monster behind you while (possibly) trying to save a helpless prisoner near the end (all while said monster is only seconds away from breaking down the doors you've shut to slow him down). Additionally, since Justine has no save points whatsoever, if you die here you have to restart all the way from the beginning!
Indiana Jones And His Desktop Adventures: Any location where you have to find your way through dense trees, with no indication whatsoever which tiles are pass-through and which are not. It's dull, unfun, and tends to take a lot of time.