Napoleon's hangover. After a rowdy night in the farmhouse, all the pigs seem to sleep in and it is eventually announced that Napoleon is dying and his last decree is to make alcohol consumption punishable by death. Next morning Squealer says that Napoleon will be making a full recovery, and the day after that, Napoleon begins reading up on brewing.
In the live action version, we get a full propaganda song lead by "a grateful duck." It's supposed to be a horrifying piece of brainwashing, but the operatic warbling voice coming from the duck just pumps so much Narm into it that you can't help but laugh.
The duckling from the 1954 film.
The animals' reactions to the revolution in the 1954 movie. When the pigeons tell a cat about it, he starts laughing hard at it as if he's saying "You're funny, man!"
The screen randomly zooming in on Napoleon in the 1999 movie as he cries "Snowball!"
Snowball's pitiful attempts at milking the cows.
Snowball: Whoops...oh, lord. Alright, I just need practice!
Napoleon takes a piss on Snowball's blueprints for the windmill.