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!