At the beginning of the game, when Skull Kid is playing with the ocarina he stole from Link, Link regains consciousness behind him and fixes him with the most hilariously annoyed, borderline deadpan look imaginable. It basically looks like he wants to say "Really? Are you serious?"
When you revive the Music Box House, the Gibdos that are swarming it suddenly return to the dust of the earth while the house plays unfitting music.
In the scene after Skull Kid leaves Deku Link and Tatl behind, Tatl goes plain insane. She starts ragging at poor Link for her troubles, but then quickly changes her mind and agrees to help him if he does the same. Link turns to the TV screen and shrugs, as if to say "Ho boy..."
If you wear the Captain's Hat and approach the King of Ikana after he sics his bodyguard on you, there's a short cutscene where he'll mistake you for Skull Keeta, the giant Stalfos who gave you the hat. But then, he remembers that Keeta was a bit taller than Link, and the battle resumes.
The Bremen and Gibdo masks have some pretty funny effects during the battle too. Wearing and activating the Bremen mask causes Link to play a marching tune on his Ocarina. The guards will stare at each other as the drums start up... and then begin marching in tune with Link's song.
If you approach the king during the fight against the guards, he'll casually stick his leg out and kick Link away without reacting at all otherwise. You can also shoot arrows at him, which causes him to angrily stand up and dodge it.
If you check outside the Astral Observatory at the Termina Field, you'll find a guy in a tree trying to snag some Red Rupees. Roll into the tree, and the guy will fall out and hit the ground with an audible thud.
Shooting Tingle out of the sky. Since Americans Hate Tingle, it's a good thing we can get a laugh out of this.
Similarly, there are carnivorous plants in Woodfall Temple that can be used as platforms. Only Deku Link can safely cross them because he is too light for the plant to detect. Regular or Zora Link will be eaten. However, if you're Goron Link, the plant tries to eat you, but Goron Link makes it explode!
Goron Link in general seems to have been designed around the Gentle Giant trope, especially the slightly clumsy handling and his amusing attacks (the third attack in his combo is Ass Kicks You).
When you go see the monkey at Deku Palace and show him your Deku pipes, he'll go on about how the Deku Princess is in danger, and all that. Then as an afterthought, he asks, "By the way, who are you?" Face Fault! (This may also be a visual gag to show that the Deku Pipes are so heavy that Deku Link just plain topples over.)
Following in the footsteps of the bickering evil sorceress crones from Ocarina, the pair of bickering undead floating heads in Ikana Castle.
Although it relies on the use of gameshark codes or glitches, transforming into Fierce Deity Link outside of the battle with Majora reveals he towers over nearly the entire population of Termina. This, in itself, isn't nearly as amusing as what happens when you trigger certain actions and events as Fierce Deity Link that fail to compensate for how he towers over the other races you become. This leads to things like the Song of Soaring making Link sprout ass wings before taking off, or him crouching just to walk into a door half his length (though he doesn't crouch so much as his legs sink into the ground temporarily).
Goron and Zora Link also have their wings during the Song of Soaring slightly below their shoulders, like they would normally be on Link, which is also somewhat funny.
In the 3D version, the Fierce Deity can be used out of the boss rooms! Legitimately! ...For the express purpose of fishing. This is funny enough on its own, but then a Hope Spot kicks in when you realize that you're still the Fierce Deity. The warp portal that takes you out of a boss room switches you back forcibly no matter what form you're using, but the Fishing Hole door does no such thing to the Deku Scrub, or Darmani, or Miaku. Maybe you can get out and wreak havoc on-
Fishing Hole Man: Hey. Hey! What's with that scary face, fella? If ya leave here lookin' like that, you'll scare away potential customers and ruin our reputation! ...Wait. Hold up. Where did ya even come from...?
Note that he says this even if you pay for your fishing session while wearing the mask. How did he not notice before?
The Versus books strategy guide for this game, if only for the commentary.
"Mere moments after mastering the power of time travel, Link uses its unfathomable power to commit bank fraud." [referencing Goht in ice] "Now, you'd think all we'd have to do is just chisel off the mask and call it a victory for the forces of good, right? Well, Link likes to do things the hard way, so take out your fire arrow and thaw the beast. "Zora Hall is contained entirely in the belly of a giant fish. There are two entrances: One is underwater, through the fish's mouth, and the other is in the back, through the...the fish's...Uh...oh my god, that's disgusting!'"
The Swordsman in Clock Town has a variety of funny responses if you talk to him in a different mask. The crowner is if you wear the Mask of Scents...
"I am not stinky! I take a bath at least once a month!"
Judging by his looks, it could be a Take That! to hippies as well.
A hilarious little moment: If you talk to the Swordsman after midnight on the third day, you'll find him cowering in the back of his shop, begging not to die. This wouldn't be funny normally, but it is when you consider that the Swordsman previously boasted that he would cut the moon in two.
If you wear the Bunny Hood and talk to the swordsman, he'll go into Cuteness Proximity mode and ask you if he can tug on your ears before composing himself and telling you "your bunny will get dirty if you train with it, so put it away".
The scarecrow under the observatory, dancing to the beat of Saria's song.
Here's an amusing trick. Epona is able to walk on the platforms created from ice arrows. Normally this is prevented by two factors: one being that the platforms only form several feet away from the shore, and the other being that Epona won't venture into the water at all. But at the far end of the beach, in the waterfall pool in the area leading to the beavers' pond, Epona can jump up onto the platform where the water is level with the edge of the rocks. It's totally useless, but this is the one place you can walk her out onto ice platforms, and then quickly get off before they melt to see her standing on top of the water (note: if you stay on her back and the ice melts, you'll be stuck and have to quit out of the game).
With careful aim, you can also have her jump and stand on top of the fence around the fisherman's hut. It's worth a giggle to look at a baby horse perched up on the wall like a cat.
The scene where Mikau gives you his last request. He lays on the ground, dying... then suddenly jumps up, whips out his guitar, and starts rocking out while singing his last request. Then he promptly collapses again and dies. Mood Whiplash at its finest, ladies and gentlemen.
"THANK YOU!" *thud*
Dawn of A New Day — The Skull Kid sniffs you.
After the heartwarming moment of watching the Elder's son fall asleep, Link looks around in surprise that all the other Gorons are sleeping too. It's obviously due to the effect of the Goron's Lullaby, but it's more hilarious if you think about it another way: they dropped asleep due to the sheer relief of not having to hear his constant crying anymore.
If you talk to the Elder's son after defeating Goht and restoring the area, he'll be by the rock blocking the Goron Races. Talk to him and he's understandably pissed about the races being blocked, but he'll promise "not to be selfish and cry"... seconds later, he bursts into tears just like before. (Thank God it stops once you close the text box!)
How do you get the Deku Princessnote Who is, shall we say, rather plump..., back to her tribe? In a bottle, of course!
If you try to sell her to the Curiosity Shop owner — who is, for reference, the guy who sells your items when that blasted vulture steals them — he will absolutely refuse to buy her.
When Link returns the princess to her father, the scene that follows is both hilarious and awesome. The King starts to rejoice, but she immediately attacks him and glares at the guards, who are terrified. What tops this moment is the Butler hopping in unison while the Deku Princess is giving a proper punishment on her father. Initially, it's easy to miss... until the moment where you can see him still doing it when the Princess asks for the monkey to be freed.
The manga ending is rather amusing. After Fierce Deity Link defeats Majora, the Happy Mask Salesman comes to collect the mask. When he looks up, FD Link glares at him, lashes out at him, and tells him to scram. Don't deny it; you wish you could do this to him. After all the trouble he caused by having Majora's Mask and forcing you to go on a quest to get it back, someone had to teach him a lesson.
The intro cutscene for the Great Bay Temple in the remake. The female pirates get dragged up by the tornado, where you can hear their varied screams. And nothing of value was lost since there's no Nabooru.
If you successfully catch all the Bomber kids, they'll tell you a secret code that allows entrance into their hideout. You can go back in time with the ocarina and get in the hideout before they ever taught you the code to begin with, and when you get out, the leader will say:
"Only the Bombers know that secret code, so why do you know it?! Listen, guy! ... ... ... You're pretty good!"
The Inverted Song of Time causes time to flow at half pace (which is an absolute lifesaver). Some characters' movements (the Postman, Sakon, Anju) are scheduled strictly. With time slowed, their movement speed is also halved... but their animations aren't. Most of the time, they'll end up moonwalking (or close to it) while you're waiting for them to perform something. The best are when Postman and Sakon are inside buildings, which will slow their movement enough to make them look like they're fighting a really strong wind.
Romani's Mask allows you access to the Milk Bar and functions as proof Link is a "grown up"... except it looks absolutely ridiculous, closer to the kind of idiotic-looking headpiece an Amazingly Embarrassing Parent would stuff their unfortunate child into. This is lampshaded at least three times — the Bomber guarding the hideout concludes that Growing Up Sucks after seeing it, the part-time shop clerk says he gave up on becoming a member because he didn't want to wear it, and the Dojo Instructor loses the will to teach if you talk to him whilst wearing it.
Finding the cow in the Gibdo Well. It has literally no reason for being down in the darkness other than one of the Gibdos wanting milk and the game is nice enough to not make you go all the way back to town or the ranch just to get some.