Belle's conversation with Lumiere and Cogsworth (after she has been treated to a production number by a singing candlestick and a veritable platoon of dancing tableware):
Belle: I couldn't possibly sleep now! It's my first time in an enchanted castle! Cogsworth:(laughing nervously as a fork skitters by on its tines)Enchanted? Who said anything about the castle being enchanted? (to Lumiere) It was you, wasn't it?! (they fight) Belle: I... figured it out myself.
Belle, aware that the townsfolk are gossiping about her, looks to her father for reassurance:
Belle: Papa...do you think I'm odd? Maurice:(emerges from underneath his latest invention wearing a bizarre contraption on his head) My daughter odd? Where would you get an idea like that?
Just look at Maurice's face after a hunk of wood clonks him when it's thrown from his chopping machine. Pure hilarity.
Belle and the Beast's argument over dinner. The immaturity of them both is what sells it, from the Beast's Big "WHAT?!", to his forced politeness and Belle's retorts.
For added hilarity, someone interpreted how that scene would go with the prince.◊
The Beast says Belle's being so difficult but tries to ask her to dinner again and when she says no again he points at the door and looks at his servants while giving them a "You see?" look.
"Be Our Guest" was hilarious on its own, especially all the torment Cogsworth went through, but one line in particular is especially hilarious.
Cogsworth:(almost in sync with the music whilst a group of featherdusters are dancing ever closer to him) Oh, gee, darn. Fun's over. Over here. (realizes they're not stopping) Line up, now! Aaaahhh! (runs for it)
Gaston: Here, picture this: A rustic hunting lodge, my latest kill roasting on the fire, and my little wife massaging my feet, while the little ones play on the floor with the dogs. We'll have six or seven.
The entire attempt at a proposal by Gaston is glorious, as he's blissfully unaware of Belle's extreme disinterest, which isn't helped by the fact that she never actually says no until she lets him out.
The hilarious facial expressions Beast makes when he and Belle are arguing about her running away, especially when he's positively dumbfounded that she's telling him off and can't think of anything to say.
Beast: If you hadn't run away this wouldn't happen. Belle: If you hadn't frightened me I wouldn't have run away! Beast:(lost for words) ...Well, you shouldn't have been at the west wing! Belle: Well, you should have learned to control your temper!
Pretty much all of 'Gaston', but especially the lyric "I use antlers in all of my dec-o-rating!" and the accompanying visual.
These lines after throwing Maurice out of the tavern:
Gaston:LeFou, I'm afraid I've been thinking.
LeFou:A dangerous pastime-
Gaston pausing while proposing to Belle to check out his reflection in the mirror. And the fish eye effect of him when Belle peers out the door to see who it is when he comes to her house to propose.
There's also Belle rejecting Gaston by opening her door and letting him fall into the mud head first with his butt sticking out after saying "I just don't deserve you!"
Even funnier in the stage version, where he responds to this with "Who does?" This is after a song where he says that women are "occasionally" useful "mainly for extending the family tree", and that "we will be the perfect pair, rather like my thighs".
The Bimbettes crying at Gaston's "wedding" ceremony for Belle because they are in love with him.
What makes it is the contrast to what happened beforehand; Gaston thanks everyone gathered for coming to the wedding reception he's set up in front of Belle's house, and adds jokingly, "But first I'd better propose to the girl!" which makes everyone laugh. Cut to the Bimbettes.
The Bimbettes "accidentally" spraying LeFou with water after he goes gaga over them. One of them actually used her heaving bosom to push down on the water pump.
After the song "Something There", Mrs. Potts doesn't want to answer Chip's question.
Mrs. Potts: [singing] There may be something there that wasn't there before.
Cogsworth telling the Beast that Belle isn't coming down to dinner.
Beast: Well? Where is she? Cogsworth: Who? Oh, the girl! (starts getting nervous) Yes, the...girl. Well, actually, she's in the process of, uh...circumstances being what they are...she's not coming. Beast:(after a beat)WHAT?!
Even before that, when the door opens, but before it reveals Cogsworth instead of Belle, the Beast's face could only be described as that of a teenage girl on prom night.
Anything with Gaston when he's not being sadistically creepy. Something about his ego and the way he talks with pride over the assumption that if he wants something then he deserves it is hilarious.
Funniest part is this after LeFou makes fun of Belle's father (which Gaston found hilarious):
Gaston grabbing Belle's book and asking how she can read it when it doesn't even have any pictures. Made funnier by the fact that it actually does have pictures, it's just that it's an illustrated storybook with a lot of text.
LeFou standing to the side and singing "Kill the Beast" as the villagers are ramming down the castle doors.
LeFou conducting the band:
Gaston: Now when Belle and I come out that door- LeFou: Oh! I know! I know! I strike up the band! (cue fast tempo version of "Here comes the Bride" which is then Cut Short by Gaston throwing a tuba on LeFou's head) Gaston: Not yet! LeFou: Sorry!
It's shown that he's still conducting the band after Gaston is thrown into the mud.
LeFou: So, how did it go? Gaston:(grabs LeFou by his shirt) I'll have Belle for my wife. Make no mistake about that! (Gaston throws him on the mud) LeFou: Hmm, touchy! Pig:(agreeing with LeFou) *snort, snort*
During Belle and the Prince's dance, Lumiere and Cogsworth get into a fight each claiming he was the one who knew it would work out in the end. Clearly Cogsworth was mostly skeptical during the film.
Lumiere: I told you they would break the spell! Cogsworth: I beg your pardon, old friend, but I believe I told you. Lumiere: No, you didn't. I told you! Cogsworth:(pushes Lumiere) You most certainly did not, you pompous, paraffin-headed peabrain! Lumiere: En garde, you... you overgrown pocket watch! (slap his face with a glove)
They waited until after they'd changed back before trading some worthy insults.
During 'Something There', Belle ducks behind a tree while the Beast feeds some birds, in order to get a gauge on the sudden new feelings she has about him. She peeks back around the tree - to find him with birds perching all over him.
She then throws a snowball right into his face after the birds fly off. When he attempts to get back by making a large snowball in his arms, she hits him with another, causing him to to throw the large snowbal into the air, which then lands right back on him.
In the stage play, Lumiere and Cogsworth are commiserating over the prospects of being cursed forever, when Belle arrives and passes by looking for Maurice. The following exchange is often played as such:
Lumiere: Oh, it's a girl. Cogsworth: I can see it's a girl. (Beat.) (Double-take.) Both:It's a girl!!!
When Belle tells Gaston to use his imagination Gaston has a look on his face like he had never thought of that before.
In the musical, during the 'Beauty and the Beast' sequence:
Belle: Dance with me? Beast: Oh, I don't know- Lumiere and Cogsworth: DANCE WITH HER!!!
Belle attempting to defend Maurice:
Belle: My father's not crazy! He's a genius! [cue explosion] [Belle runs back home as Gaston and LeFou laugh]
A tiny moment that will go unnoticed unless you watch the film dozens of times, but in "Be Our Guest" Belle's chair is all ready to tie a napkin around her neck. Belle intercepts the napkin and puts it in her lap instead. The chair puts its arms at its sides in a clear gesture of "Well I never!" See this here.