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:
Lumpy: "There's only one creature capable of making a footprint that size." *Dramatic Pause* "The Abominable Snowman."
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 T-Rex, and Kong's fight with them (when it's not being HONF, 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 f*ckin' weird, it's gonna blow your balls off."
Black's "song" that he'd been working on (roodle-y doodle-y doodle-y doo...).