The Bomb Bag pickup text. "You found bombs inside! Now you can set them to C and blow stuff up! What a lucky guy!"
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.
There's something humorous about young Link playing Epona's Song and getting pushed by Epona.
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, as if Darunia is trying to become a seductive God.
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!!
To top it off, that cutscene is the longest in the entire series, at a staggering sixty seconds. A whole minute's worth of Ouweep.
Actually, this cutscene isn't the longest in the series. It's not even the longest in the game. The sequence in which Zelda grants the player the Light Arrows last at least six minutes, which is why many speedrunners affectionately refer to it as "Long Ass Cutscene".
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.
If he stands on the mechanism of the Windmill Hut long enough, Link starts to get woozy.
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.
Naming 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!
After you get the Goron mask from the Happy Mask Salesman, put it on and talk to any Goron and they'll think you're a child Goron. They even tell you to make sure you eat your green rocks.
During the start of the game, Navi (somehow) bumps into one of the holes in the fence. She also says "Hello!" to the girl who teaches Link Z-targeting (L-targeting in the GameCube version and the 3DS remake).
There's a crazy Goron who loves rolling down Death Mountain, leaping into the air when he's about to stop and landing with a BOOOOOOOOOOOOOM!!! Bonus points for funny if you happen to be squished in the process.
Whenever Mido is acting as an NPC Roadblock, you can engage in some vaudeville-esque slapstick by getting him to waddle back and forth as he mirrors your movements to block you from going forward a la "monkey see, monkey do".
Some of the pits you can bomb open have inexplicable cows in them.
Navi's hints may be annoying to some, but there's something legitimately funny about seeing Navi's hints for a specific area while you're at that area. For example, her wondering where Zelda is even though she's right in front of you, or telling you to go to Kakariko Village to get the item Sheik told you to get while you're in Kakariko Village. Looks like even fairies can leave their contacts at home.
One house in Kakariko Village has the back door closed if you go in as a child. If you try to get inside, the person in the house will scold you about how only bad children try to sneak through the back door... before he immediately decides you're perfect to share some gossip with.
Hearing Darunia's son (who is named after whatever you name Link) talk about how much he loves his name can be downright hilarious if you choose to name Link something ridiculous.
It's possible to fight Ganondorf in his first phase by using a Bottle to deflect his attacks back at him.
When you light the last torch that makes the giant jug in Goron City start spinning, Link spins in place for a couple of seconds, as well. One gets the impression that it's a bug they left in because it's funny and doesn't hurt anything.