Level 29 in Heart Star is a level where Heart must carry Star up a vertical hall of spikes, and vice versa. However, in order to move while carrying, you have to switch to the world of the carrier. This results in you having to use trial and error in order to cross. And the game never tells you about this.
Level 27 in Chromatron was a massive Guide Dang It moment, as any level further that used the same trick. Not exactly unfair, but a way too obtuse puzzle: there is the object called quantum tangler, and if you change the color of the beam on one side, the other side also changes color — the opposite way. But no matter what you do, you cannot solve level 27 and a few others until you realise that reflecting a quantum-entangled beam BACK ONTO ITSELF causes very insane color changes. There's no indication in the game that you can do this, and the only similar thing was on level 17, where with a splitter it's pretty apparent.
The entire Myst franchise is essentially a huge set of these. At a bare minimum, be prepared to take a lot of notes.
Supaplex, a perfectly logical Boulder Dash clone... until you get to levels 59 and 60, and later on 100 and 108, and even on 91, but you can work around on that one. A corridor three tiles in height, which has three vertical rows of rocks one after the other and only the last rock can be pushed. No matter what you do, there doesn't seem a way to get past, because only one of the top rocks will fall. The solution? Eat all the tiles near the first row of rocks, but eat the middle one last, then step away TO THE SIDE — two rocks will fall as opposed to the usual one, which in turn will free the second top rock to roll off. The last rock can now be pushed. The only hint you were given is an in-game demo which does something similar on a completely different level and stuffs it up 30 seconds later. At this point, most people already know that the demo feature is pretty useless, so they miss it. Guide Dang It.
That said, the above puzzle can be solved simply because there are few enough possible sequences of moves that you can just try everything. Similar remarks apply to the infamous Guide Dang It on Repton's tenth level, "Octopus". One puzzle requires stepping to the right from under a rock, then immediately pressing left so that you push it aside as it falls, preventing it trapping a diamond directly below. (Nothing up to this point hints that this manoeuvre is possible.) Many players did discover this by themselves just because nothing else could possibly be the solution.
Karoshi 2.0. This is mostly due to the game Breaking the Fourth Wall, the kicker of which is level 48, on which to get an in-game CD player working, you had to insert a music CD in your computer's CD drive. Who would've thought of that?
The game is overall pretty simple to figure out in what to answer to get the Karma Meter to lean right or left or remain in the middle. The guide-dang-it comes to the final stage, when the player is asked questions that don't influence the meter - the answer to those question determines what ending the player gets. Nothing tells you the exact answers you need to give, to get a certain ending. Fortunately, the answers are indicative of things.
Getting the True Freedom ending. The regular Freedom ending was simple enough if the correct answers were given for the last stage's questions, as your position on the meter was irrelevant. The True Freedom ending requires the player to keep the meter at the gray area in the middle of the meter. No question asked or text sent in the game has a neutral option, it always leans either towards Chaos or Law. So the player needs to make sure to always answer one direction, then the other, which is difficult enough as it is.
Keeping all the NPCs alive for the week. This requires Vincent to talk to them either at the bar or during the nightmare stages, while giving only certain answers. If the player screws up one of those questions, the character will end up dying. Annoyingly difficult to begin with, but an extra guide-dang-it belongs to Archie and Todd. If one of them dies, the other will, too, regardless of your answer. They both need to be kept alive. Especially Todd has a trick-question midway through the game, which can easily trip players up. Hope you have a guide handy.
The tea system in Professor Layton and the Diabolical Box: figuring out the correct combination of three teas out of eight (including repeats) is nearly impossible on the first try from the characters' usually incomplete instructions. Doing it on the first try is necessary because if you give the NPC a cup they don't like, they won't even want tea anymore for a while.
Chulip has such obscure clues (and one requiring familiarity with Japanese/Chinese counting systems, no less) that it comes with its own guide, and even then one clue is not entirely accurrate.
The Switch Inferno level in Super Monkey Ball 2. It is indeed a switch 'inferno', since there are many dozens of switches laid out on the floor, and there are no initial clues or indications for the correct switches that can reveal the goal. Press any of the wrong ones, and you get smacked by a fast-moving wall, possibly knocking you out of the course. Your only help is that when you hit a wrong switch, all the wrong switches will light up, so the correct ones can be easily determined for future reference.
Freeware indie games are in no way exempt from this. Braid may be one example, but at least the Guide Dang Its weren't crucial to finishing the game. Opera Omnia gives you a handful of them, one of which is understanding the mechanics (the butterfly effect in reverse), another is Chapter 18 (you have to use what is technically a bug to win).
Scooby Doo: Showdown in Ghost Town requires you to open a bank vault door, but thanks to fixed camera angles you can't get a good look at the door. If you decide to use a clock on it, then you can see the writing indicating that it's a time-activated door, and the slot from which the previous clock was long since looted. Less than intuitive for a pseudo-Wild West setting, and bad game design given that you probably used the clock after every other item failed.
Using this ability at any other point in the level makes the level Unwinnable. This is not hinted at anywhere.
There is a small way to figure it out in the DS version, though - if you made it to this point without using the Healing Touch, the marker on the bottom left (that you double-tap to ready the Touch) remains a star and visibly regenerates back to full. Stiles also mentions having to concentrate just a little more, as well. Then again, you're probably more focused on Savato and the 25-vital damage per shot.
Spellbound Dizzy is legendary for its level of difficulty. To rescue each of your seven friends, you have to find 5 magic stars and a possession of theirs, a process which involves hours of fetch questing and some damnably Nintendo Hard trial-and-error gameplay (how are you supposed to figure out that you have to drop a pepper pot on a whale to make it sneeze, so you can jump up the spout of water to access some hidden rooms you didn't even know were there?? Or that to access another hidden room you need to flood the pumping station you're in by smashing a plug with a hammer???)
But that's not even it! Once you've rescued everyone, you're given some string and no further explanation. To get to the TRUE end of the game, you have to assemble a kite and let the rush of air from an old mine shaft carry you up into the sky. All the components are in their own impossible-to-find hidden room (one is even hidden behind a wall panel in a hidden illusion room that's near-impossible to get out of). At no point, here or throughout the game, are you given any indication of what you're looking for, where it might be and what to do with it once you've got it. And there's no map.
Alchemy is a small mobile game available on Android, in which you have to combine elements (starting with four basic ones - earth, fire, water and air) to get a wide variety of other elements, up to 360 in total. All well and good, but the game is absolutely impossible to complete without consulting some form of guide, because many of the combinations are either obscure enough or crazy enough that the average person is unlikely to have heard of them. For instance, to get "petroleum", one must combine kerogen with pressure. Which is, well, factually true, but who would know offhand what kerogen was unless you were like me, saw it in a cheat sheet for this game and Googled it? And some of them don't make any intuitive sense - for example, water + earth = swamp. However mud = water + dust. Who, when they think of what goes into mud, thinks dust?
Chip's Challenge. The first 30-50 levels can be beaten after solving puzzles and obstacles that rely on basic mechanics. Further levels, however, will resort to more advanced means, and some of them (like Perfect Match or Partial Post, whose hint tiles aren't clear enough!) will likely leave gamers stuck for a long time. Then, of course, there are the convoluted and mind-screwing mazes that will inevitably call for a step guide.
The Settlers of Catan knockoff you can find lying around. Unless you've memorized the cost of all buildable resources, let alone how the game works in the first place, it's terribly difficult to play since the game doesn't tell you anything about it.
The mechanic of the orange triangle symbol can be hard to ascertain as puzzles with those are at first only found in oft-obscure locations across the map. This becomes a problem later in (and when trying to open)...
...the Underground Maze. The same mechanic allows the player to turn the fence at the beginning back on, with the solution to that problem being found within the Underground Maze.
The game generally does a good job of giving you sufficient clues to the solution of any given puzzle, but there are definite exceptions. The puzzles in the jungle, for example, appear to have no visible cue, and that's because they don't; they're the only puzzles in the game (with the exception of one in the Keep and the infamous Red Door puzzle) that rely on an AUDIO cue, specifically the chirping of birds in the background.
It's pretty safe to say that a 100% completion of the game is effectively impossible without looking up walkthrough instructions. Many of the optional puzzles (such as environmental monolith patterns) are so deeply obscure and may require such actions and timing as to be essentially impossible for a single person to find out in any reasonable amount of time, no matter how dedicated.
The Talos Principle: Some stars are relatively straightforward, while others require some pretty outside the box solutions. Numerous ones require exploiting the design of two or more puzzles. Even when parts of the solution are obvious, actually getting everything in place is another story.
The very first level's involves walking into what looks to be a turret's firing radius; ignoring an area which seems like a small positioning challenge but is actually a red herring; skirting the turret's firing radius once again; and bringing a jammer you find near it halfway across the map, to a courtyard that can only be accessed by flipping a hidden switch with no indication it's there.
One of the stars requires you to use tools not available in the game itself, making this a rather explicit case of Guide Dang It. The solution requires you to find out what a certain QR code is saying, as the game itself does not tell you; you'll have to use some external means for this, like a cellphone. After that you need to figure out that the numbers given in the text are ASCII codes, and to find out what those ASCII codes mean, again something the game itself doesn't tell you.
The A4 star was enough of Guide Dang It that it was actually revised in a patch prior to the Gehenna DLC, making the solution slightly more obvious. Amusingly, this turned it into a Guide Dang It for players who had previously figured it out, as the original solution was rendered non-viable because the laser connectors needed to achieve it no longer align from puzzle area it used to connect from. In the original, a laser connector was hidden in a tree outside the first puzzle area. The trick is to guide a red laser to the tree from the adjacent puzzle area, which then allows you to trigger the forcefield to get the star. In the revised version, the connector is now visible on a pillar but further away from the first puzzle area, so the only red connector in view is in the testing area at the far back.
The secret room in chamber A7 has a lock which requires placing two energy balls in 2 specific containers out of 25. Outside of brute forcing it (which, given the high number of possible combinations, would take an extremely long time), the only way to learn the combination is finding a photograph in the Bio-Lab which shows it. This photograph is found long after you've left behind said room, which means it's only accesible when replaying the game.
Similarly, entering the captain's room requires finding the code, which is found in a sheat of paper in the maintenance station, again long after you've left behind said room.