In the Spirit Temple, when the miniboss battle with the huge Iron Knuckle is about to begin, a single chord of the miniboss battle music plays, at which point the Iron Knuckle realizes that it doesn't have its gigantic axe, so the music stops, the Iron Knuckle snaps its fingers to summon the axe, and then the battle theme starts over and the sequence properly begins. It's just so out-of-character for the game, like something out of Looney Tunes. See it here.
Darunia gettin' down tonight when you play Saria's Song, complete with psychedelic background!
Darunia: What a hot beat!
If you look during that sequence you can see Link back away very slowly in response.
The ending of the Dodongo's Cavern in Ocarina of Time. Darunia decides that he and Link are now Sworn Brothers, and gives him a hearty pat on the shoulder... which knocks Link to the ground. After Link recovers, he decides to celebrate his and Link's new brotherhood by giving him two gifts. The first is the necessary Plot Coupon, the Goron's Ruby. The second? A Goron Group Bear Hug. Cue Link running off screaming.
Link's reaction to seeing Ruto after seven years. His facial expression is priceless.
Ruto: It's me, your fiancee, Ruto! Princess of the Zoras!
When you finally get the Zora's Sapphire from Ruto, she says you have to marry her now. The following narration is hilarious. Paraphrased, it goes like this: "You got the Zora's Sapphire! Ruto says you have to get married. You're not quite sure what she's talking about, but..."
After the defeat of Phantom Ganon, Ganondorf's last bit of the text:
Ganondorf: What a worthless creation that ghost was! I will banish it to the gap between dimensions!!
Koume and Kotake, the witches collectively known as Twinrova, arguing after they've been defeated.
Koume: I'm only 400 years old!
Kotake: And I'm only 380!
Koume: We're twins! Don't try to lie about your age!
While that particular part takes the cake, the rest of their argument is pretty funny as well, especially considering the fact that they seem to be more concerned with bickering with each other rather than they fact that they're dying.
That's no way to talk to your older sister!
Ingo's groveling when you come back to the ranch after defeating him.
You got the Megaton Hammer! Use it to smash and break junk!
Ruto gets a little too close to Link following the defeat of the jellyfish in Lord Jabu Jabu's belly and causes Link to freak out and move away so that he accidentally falls into the water.
The freaked out reaction from the head of the Skulltula House when you show him the Mask of Truth.
The Carpenters in Kakariko Village look pretty tough, but when they walk, talk, or do anything else, it's pretty clear that they're not just Ambiguously Gay.
Link's idle animations are pretty fun to watch, especially in the ice dungeon where he'll shiver and sneeze. Equipping the iron boots and hearing their loud clanking is also pretty funny.
On that note, just seeing Link walking in the Iron Boots on land is funny. He's clearly struggling with the weight.
If you equip the Iron Boots before entering Kakariko Village when it's on fire, he will run at normal speed but the clanking sound will still play.
During the Mask-Selling sidequest, when you give the Spooky Mask to the kid in the graveyard, this text box pops up:
You charged him the full price of 30 rupees?! And he didn't even mind paying!
Being ambushed by cuccoos. As irritating as it may be sometimes, there's no denying how absurdly funny it is seeing Link getting his butt absolutely handed to him by a bunch of squawky chickens.
Calling Link Zelda
"Zelda... Strange, it sounds somehow familiar."
One of the Gorons in Goron City has this gem. It's basically proof that Gorons don't go outside much.
Goron: Oh? We don't get many visitors way up here. Where are you from? The forest? What's a "forest"? It's where a lot of "trees" and "plants" grow? Now I'm even more confused! Nothing grows around here besides the Bomb Flowers... We don't have "seeds" or "nuts" around here either. Even Deku Sticks are very scarce around here!
During the start of the game, Navi (somehow) bumps into one of the holes in the fence. She also says "hey!" to the girl who teaches Link Z-targeting (L-targeting in 3D)