I haven't responded to this before because it's an enormous question worthy of a thesis. I enjoy all three of the classic teams (you left out the Stooges...too low-brow?), but all of them have some goodies and some stinkers.
Until we get some more responses, I'll just say that my fave Marx Bros. are
Horse Feathers and
Duck Soup. They are both completely insane, and neither is over
70 minutes, so even if you have a low threshold for Depression-era puns, you'll laugh yourself silly with those two. Just thinking about Groucho's Biology lecture concerning the white phagocytes in between the spitwad-shooting contest, while Chico asks "when are ya gonna cut the watermelon?" makes me all happy, but hell, you already know I'm weird.
My favorite A&C is
Abbott and Costello Meet Frankenstein which is both a comedy and horror classic with not only Frankenstein's Monster (Glenn Strange), but Count Dracula (Bela Lugosi), the Wolfman (Lon Chaney, Jr.) and the Invisible Man (Vincent Price)! For some reason, these idiots want Costello's idiot brain.
The Time of Their Lives, which involves Bud and Lou as Revolutionary War-era ghosts in the 1940s trying to make amends for an earlier mix-up, is their other film which really stands out to me. Yes, it's funny, but it's also a highly creative fantasy, and once again, it's got scares! Anybody who wants to see a terrific version of "Who's on First?" is hereby directed to
The Naughty Nineties, a cute riverboat gambling flick which is completely upstaged by the hilarious routine performed on the stage of the riverboat.
I enjoy L&H, but their shorts (i.e.
The Music Box) tend to be even better than their features. I guess my favorite full-lengths are
Way Out West, a funny western which is aided by the anomoly of the pair on an important mission in the Old West, and
Sons of the Desert, which I first saw over
40 years ago at my elementary school! Once a week, we used to have 10 cent movie shows after school. You'd get a bag of popcorn, sit on the floor, and watch a flick! This one had L&H telling their wives stories so they could sneak off to a lodge convention. Needless to say, they get screwed (although I didn't know that word back then

), and not in any good way.
"Naked Woman, Naked Man
Where did you get that nice sun tan?"