Duck Soup is the best Marx Brothers movie. Animal Crackers, A Night at the Opera, and most of their work from that era is also pretty great.
I don't know WC Fields as well as I'd like to but It's a Gift is a great example of the era where actors were transitioning from silent films to talkies and from shorts to features. The Music Box occupies a similar position in Laurel and Hardy's career.
Going back to the silent era, Steamboat Bill Jr is the best-known Buster Keaton feature, and it still holds up. Even if you've never seen the movie you've seen the part where the front of the house falls down around him -- and even if you've never seen the original, you've seen it homaged somewhere.
One Flew Over the Cuckoo's Nest is a classic too, and I think it definitely qualifies as a comedy despite (or because of) its edge. (While we're on the subject, I'd list another Milos Foreman movie, Man on the Moon, as the best Jim Carrey movie.)
And we've been working over the Mel Brooks library but nobody's mentioned The Producers yet. That should definitely go on there. I'd tip the original Mostel/Wilder version, but the musical is solid too. (Better live, though.)
Back to the Future's great. I'd say The Jungle Book is my favorite animated Disney movie. Most of Pixar's oeuvre qualifies as great comedy too.
And while the Pink Panther series ran too long and was definitely a case of diminishing returns, the first few films are still great.
And talking of long-running series of the like we don't really see anymore, The Thin Man is still a lot of fun to watch.