In the original game, if you pick up a Clock in a room with Wallmasters, they will get stuck in the wall. If it happens to be a room where the doors are locked until all enemies are defeated, your only option is to reset or use the "quick end" code.
Due to all kinds of glitchy stuff in the game it's possible to glitch Link into the floor at the start of a palace, glitch the floor so Link keeps falling through it, get Link stuck in the middle of an ocean and all kinds of other stuff where the player's only option is to reset or use the "quick end" code (which isn't even possible when stuck in the ocean). In Nintendo's defence, some of this requires stuff that wasn't even possible on the original console, like pressing up and down at the same time, and other glitches require the player to do things that most normal players wouldn't think of doing, like talking to the same character several times in succession and then entering a door on the right frame.
In the three palaces where blocks fall to form a wall, you can climb on top of the wall, jump, and activate the Fairy Spell to go to a glitched palace. The layout will be the same as the first palace but the color and texture of the walls will be the same as the palace you were originally in. If, for some reason, you have not completed the first palace, you will find Horsehead at the end. If you defeat this Horsehead, the game will register as you having beat the first palace, but not the palace you originally entered. However, when you exit this glitched palace, you will find that the palace you originally entered will be destroyed as if you had completed it. If you happened to save, you will be unable to finish the game, and you will have to delete your character and start over.
If the player tries to complete palace 3 before collecting the Handy Glove in palace two, you might get stuck in an early room. Breakable blocks fall down on either side of a large floating platform near the ceiling. If you stand beneath the platform, the breakable blocks can wall you in on either side, and since the floating platform protects you from falling blocks above you, you can't even take any damage to die and restart the room.
Link's Awakening was notorious for a door that could only be unlocked with an Interchangeable Antimatter Key. The door in question was located across a moat that you were meant to cross after gaining the ability to swim. The designers failed to realize that Link could just barely clear the moat by jumping, leaving him with neither the swimming ability needed to finish the dungeon nor the key needed to get that ability. The DX version fixed this by making the jump impossible.
You can also get stuck in Eagle's Tower in the original (non-DX) version. If you drop one of the orbs down a certain hole, then it won't respawn properly, preventing you from completing the dungeon.
It's also possible to drop the orb behind a pillar and on spikes, rendering it impossible to retrieve it.
You can also trade your shovel for the boomerang, and then another shovel will appear in the shop. Buy this shovel, and then your inventory will be too full in the last dungeon to pick up the Fire Rod, which you will need badly. This can be rectified by using up all your Bombs or Magic Powder, thus freeing an inventory slot... but without Magic Powder, the final boss becomes unbeatable...
The infamous "Map Glitch" which allowed the player to skip whole screens at a time would, in theory, make the item Fetch Quest easier. However, due to a glitch in the programming, only the next item in the player's quest will be available. Skipping ahead to the final item (the magnifying glass) if you don't have the second-to-last item when you arrive there, your next item will be sitting there. You will have a very hard time winning the game from that point, since you will not be able to complete the maze at the end without either brute-forcing every combination of moves or using the very same glitch to warp directly into the final boss's room. Also, if you are unfortunate enough to save the game inside the magnifying glass cave after performing said glitch, you will never be able to leave since the mermaid statue is still blocking the entrance on the overworld.
Farting around with this glitch in caverns has a pretty good chance of dumping you into a facsimile of the sixth or seventh dungeon long before you're supposed to enter. If you try to exit, you'll wind up stuck in the dungeon's still-hidden entrance and unable to move. This and the above are all good reasons to not experiment too much with the glitch until you've learned the Manbo Mambo and can warp out of these unwinnable situations.
There's a room in the mountains that can be entered through a hole in the ceiling into some water. Normally, it's impossible to get to this hole before being able to swim, but the screen jumping glitch allows you to get to it earlier. If you fall through the hole and hit the water without the swimming ability, the game will respawn you (without taking away any health) at the room entrance. Since you entered the room by falling from above, you respawn in mid-air and fall into the water again. You end up caught in an infinite loop of respawning and falling back in the water. Since you never hit the ground, you can't even use items to warp out of this situation.
Thanks to a glitch in the game, players can turn any item in their inventory into a bottle. This is generally regarded as very helpful when used for useless things like the receipt for the Biggoron's Sword. If it's used on something you actually need, you are SOL.
Jabu Jabu's Belly had switches to raise and drain the water level, allowing you to move up and down through special holes in the floor. However, if you forgot to collect a certain key before raising the water level to maximum, you will be unable to reach the boss because there's a row of locked rooms between you and it. Unfortunately, you would have to move blocks to get to the draining switch, but said blocks are underwater and you can't push blocks when you're swimming. However, this can be avoided where the second blue water switch is, you can push a block to get to the red switch, which drains the water.
In the Wii version, there's an infamous glitch where saving and quitting at the scene where you find the big cannon before talking to an NPC makes the game unwinnable. Several known workarounds exist to allow players to talk to the invisible NPC and allow them to escape the "unwinnable" situation.
There's a game-halting bug that occurs in both versions. After crossing the Bridge of Eldin and bombing the rock wall, a piece of the bridge will be warped away to somewhere else. If you happen to save and quit between here and the Twilight, then you can be reloaded on the wrong side of the broken bridge with no way to get back across.
This can be fixed, but it requires a bit of glitching of its own. Video here.
It's possible to use the hammer to enter the Goron Temple without first becoming an honorary Goron. If you claim the pure metal without doing that, then your fairy won't let you leave until you become a Goron... which you can't do because one of the Gorons grew up. You can no longer talk to every Goron, which is one of the requirements for becoming one. But it's totally worth it because you get to see two Gongorons.
The Song of the Hero quest can be made impossible to finish should the player speak to Golo the Goron a second time in Lanayru Mine, after getting the Thunder Dragon's song, but before going to the forest or volcano regions. If you save instead of loading an earlier save, prepare to restart the whole thing. Luckily, it's easy enough to avoid, and Nintendo has posted a free downloadable channel that corrects the save corruption.