I’m glad someone mentioned The State. They are awesome.
Python is up there, of course.
Marx Brothers.
For two person teams:
Burns/Allen
Abbot/Costello
Penn/Teller
Does this count:
Mel Brooks and Gene Wilder?
Brooks movies without Wilder and Wilder movies not written/directed by Brooks are never as good as the two together.
Dare I say Jeff Dunhan and Peanut? 
<g,d,r>
Sticking to the topic…great routines and duos…
Harvey Korman and Tim Conway for the “Dentist” sketch on the Carol Burnett show. Tim at his very best and Korman failing miserably not to laugh. I dare anyone not to laugh as Tim consistently sticks himself in various parts of his body with Novacaine accidently. I swear to god, funniest damn sketch I ever saw.
Abbot and Costello in the “Jewel Thief”. A thief hides a diamond necklace in a bottle of ketchup, which Costello spreads on his hamburger without noticing. The rub is the off camera sound effect of Costello biting the burger, that being those little wood carriers that hold strawberries being smashed to bits. The gigantic CRUNCHING sound along with Costello being both surprised and cracking up is priceless.
Another “Dentist” 3 stooges - One with Shemp and the boys playing wild west dentists. A old man comes in needing the drill and Shemp puts on some of the most myopic glasses imagined. As Moe and Larry hold down the old codger, Shemp proceeds to drill everything in sight: his own hand, moe’s mouth, larry’s head, moe’s nose, the old codger’s head, a foot, the chair, and shemps own mouth. Very Vaudvillian.
Can’t belive nobody’s mentioned Dan Rowan & Dick Martin! Of course, they’re best known for Laugh In, but they’ve done a couple of movies together.
IMO. the Stooges rule, and Curley is funnier than Shemp. Curley has a sense of “joyful foolery,” as it were, and Shemp just doesn’t have that. The short where a professor tries to turn the Stooges into “gentlemen” makes me roll on the floor every time.
Larry (learning to read): “Oh see the little deer. Does the deer have a little doe?”
Curley: “Sointanly! Two bucks! Nyuk nyuk nyuk.”
Groucho and the gang come in second. I was never into Laurel & Hardy and Abbott & Costello.