Team America: World Police, which I count among my favorite movies of all time. I can't think of another film that would deliver a harsh, yet accurate and in a way reassuring analysis of world politics in such scathingly scatological terms. If you've seen the film, you know what I mean. It's a perfect combination of absurdist, dark, shock and juvenile scatological humor that tickles all my funny bones.
On the complete opposite end we have Wallace and Gromit: Curse of the Were-Rabbit. Perhaps no other film outside of Studio Ghibli productions makes me feel as happy. It's so lovable, cute and warm through and through, the humor both visual and verbal is so perfectly delivered and clever yet in such good spirit towards everyone I can't really think how anyone could dislike it.
In rapid fire visual and slapstick comedy The Lego Movie and Naked Gun are my favorite examples. Not that much to say, they don't really get old.
Big Lebowski for the absurdity. It breaks so many conventions of cinema and even basic narrative storytelling that in theory it shouldn't work on any conceivable level: None of the characters have an arc, nobody really learns anything, like 80% of the narrative threads just drop off the movie completely unresolved, there's essentially no structure to the story at all, it more like stumbles from scene to scene and so on. Yet once you accept the absurdity, it's a nearly unmatched riot, and an exceedingly rare example of a comedy that actually gets funnier the more you watch it.
And in the final outskirts, in the very edges of comedy, in the strange nether, are things like A Serious Man, and a little known Finnish sketch show called Ihmebantu. Things that push themselves to such degrees of strangeness and unnervingness you no longer know if you can even call it comedy. Where the laugh comes not from finding things funny, but because it's the only reaction you can think of. Scenarios that could in and of themselves, without altering a single frame or audio cue, be presented as horrifyingly depressing, dark and downright dehumanizing. I guess I'd characterize them as skirting the edges of the Uncanny Valley of comedy: you can't really say if it's funny, yet you don't find it altogether off putting either. Such things are rare, and ever more rarely done well, but when they are, they're unlike anything else.