The protective suit Pleakley puts on in "Spike" (to protect himself from Experiment 319's spikes). The faces everyone makes in response are priceless. (Nosy's especially)
This line in "The Asteroid," after our heroes discover an old hermit on the asteroid, while on a mission to destroy it to prevent it from colliding with Earth. The line isn't just hilariously ironic, it's made even funnier by how nonchalant and blunt Jumba is about it.
Jumba: (cheerfully) "Hello! We come in peace to blow up your home!"
A lot of the random things Stitch does in the background of episodes, either getting hurt accidentally or misbehaving in some way that the other characters sometimes never even notice.
A fun example happens in "Retro," where while Nani is talking to the entire family Stitch just wanders off while her back is turned and eats one of their potted plants. Cut to Lilo giving him a Death Glare. A few seconds later, Lilo is talking to Nani again and Stitch just quietly spits the plant into the pot.
Most of "Shoe" is funny, thanks to the horrible bad luck the titular experiment wreaks upon the entire cast: the whole thing is Amusing Injuries incarnate. Special mention goes to the scene where Lilo is trying to figure out how to help Shoe, while Stitch watches from the windowsill - by the end of the scene, Stitch has been knocked on the head, fallen out of the window and had his fingers smashed upon trying to climb back in. The best part is the final battle with Gantu, however, which quickly turns into a game of "how bad can their luck possibly get?" Highpoints include Gantu being strapped to a hot air balloon and floating in front of a skeet shooting competition, and a random spurt of lava forming at Stitch's feet out of nowhere.
In "Heckler," the titular experiment spends the entire episode mocking everything about the characters - in many cases hilariously. The gold comes when he takes the mickey out of the series' nigh-constant use of it's two favorite phrases.
Heckler: "Again with the 'ohana' and the 'one true place!' I see you've read the dictionary of two phrases cover to cover!"
Stitch unsuccessfully attempting to get in on Lilo's thought process in "Clip:"
Lilo: "You look like a hairy hairball... and you seem to like to eat hair... and you're made of hair... so I'm going to call you..."
Lilo: (as though the very idea is ridiculous) "No! 'Clip!'"