After Denham and Hilda meet and befriend "Little Kong". The much friendlier giant ape fights a giant cave bear to save them. Denham bandages Little Kong's injured finger in return. The way he marvels at the bandage is too silly and adorable for words.
In the 2005 version, Kong himself, while a pretty fierce individual, has some moments of hilarity, such as his getting bored with some of Ann's antics halfway through, the temper tantrum causing a rock to fall on his head, and his nonchalant dismissal of Ann after saving her from the V-Rex.
While searching for Ann, the group comes across one of Kong's footprints, leading to this:
Bruce Baxter is enraged at Jimmy's graffiti on his movie posters...until he starts thinking about what he might look like with a mustache...
Ann's interactions with the V-Rex, and Kong's fight with them (when it's not being terrifying, that is).
Admittedly not part of the movie officially, but the outtakes feature Jack Black doing Carl Denham's scenes...as Jack Black. Specifically, addressing the studio heads about the map.
Black/Denham: "A primitive world, never before seen by man. A place so fucking weird, it's going to blow your balls off."
Black's "song" that he'd been working on (roodle-y doodle-y doodle-y doo...).
Some of the Production Diaries for Peter Jackson's film are quite hilarious. There is one that is essentially a day in the life of the featured extras, which mostly involves them hanging around the lounge waiting to be called onto the set. In the end only one of them gets to actually be on set that day, and when he comes back he brags that he actually had a line. Cut to two others (humorously) beating him up.
Jed Brophy: Had a line, didja? Hope it was a good one! ::punch punch punch::