The end of the Executioner chase where Alice runs into a clearing, finds and eats the "Eat Me" cake. The Executioner runs in, ready to attack, then Alice grows to massive size. Cue an Oh Crap from the Executioner who drops his scythe (and his jaw.) before he meets the underside of Alice's shoe.
Personally, this troper thought this exchange was funny (mainly due to Carpenter's motor-mouthed response):
Carpenter (to Alice): You need to deal with these sailors. It's your time.
Walrus: Time? Time? The time has come to talk of ships and, and, and vegetables and royalty and, and, and whether pigs have wings...and so on.
Carpenter: Enough of that, Walrus. Youstartwailingabouttherebeingtoomuchsandonthebeach, I'llhaveyourblubberforbreakfast!
Alice summarizing the Carpenter's Oyster Show, just before everything goes wrong in a most disturbing fashion.
Whenever Alice interacts with the Hatter... while wearing the Hattress Dress. Seeing the reassembled Hatter leaping from factory to factory with a tiny female version of himself clinging to his back is equal parts funny and adorable.
The first "boss" fight with the The March Hare and the Doormouse can give a few laughs and/or aggravation to the player. Alice, and even the player, is prepared for their first boss fight with a big mechanical monster, but immediately, a giant tea pot falls on them and knocks them out completely. The way they fall out is comical at best.
It's subtle, and you almost have to be listening for it, but when Alice smashes the first of the Queen's hearts when she's Giant, you can hear the Queen say "It's only a flesh wound."