WALL-E bringing EVE to his home and showing off his collection is an extended exercise in hilarity. Highlights include EVE solving the Rubik's cube and WALL-E's dance with the hubcap.
Basically everything that happens on Earth in the beginning of the movie is either heartwarming or hilarious.
That voice that says "FOREIGN CONTAMINANT".
The best part of that is the realization that they all end up on a place made of "FOREIGN CONTAMINANT".
The fact that a robot made for the sole purpose of typing uses hunt-and-peck.
M-O: "WALL-E!!...oh!"
WALL-E, in the escape pod, patting the seat next to him as an invitation to EVE.
And then his exploits trying to get the pod to stop. The thing looks absolutely ridiculous as a result of all the buttons he pushed.
In the trailer: "Seven hundred years into the future, mankind will leave our planet, leaving Earth's cleanup in the hands of one incredible machine." Cut to WALL-E smacking himself in the face with a paddle ball.
M-O jumping off his guide line, just so he can get to do his job. He prepares for it like he will blow up if he leaves the line, but all he gets is a little buzzer. It's his little evil-like laugh that sells this moment.