Title says it. At least two people, please. Up to whatever number stays together most of the time. Monty Python is an example of the latter.
A starter group:
Nichols and May
Jeeves and Wooster
Rowan and Martin
Burns and Allen
Martin and Lewis
Stiller and Meara
How quickly can we hit 100? 
Bob and Ray.
Second City
The Kids in the Hall
Upright Citizens Brigade
Mel Brooks and Carl Reiner
The Smothers Brothers
The Marx Brothers
The Three Stooges
Did you really mean to include fictional characters? Or were you thinking of Fry and Laurie?
To get some of the classics down:
Laurel and Hardy
Abbott and Costello
The Marx Brothers
The Three Stooges
The Ritz Brothers
Thanks for the fix. Fry and Laurie was who I meant, but I have minimal acquaintance with them (either way). Just names I thought of – and wouldn’t vote for. Sorry!
Flanders and Swann
Peter Cook and Dudley Moore
The Goons
Key & Peele
Mitchell & Webb
Bob & David (Odenkirk & Cross)
Rik Mayall & Ade Edmondson
For that matter, Beyond the Fringe - Wikipedia 
Cheech and Chong
Amos & Andy
Pryor and Wilder
Monty Python (to make it “official”)
The Seinfeld cast
Garry Shandling, Jeffrey Tambor and Rip Torn, The Larry Sanders Show
Carol Burnett, Tim Conway and Harvey Korman, The Carol Burnett Show
Lucile Ball and Desi Arnaz
Gene Kelly and Danny Kaye
The Bickersons ( Don Ameche and Frances Langford)
Burns & Schrieber
Allen & Rossi
Thelma Todd & Zasu Pitts
Thelma Todd & Patsy Kelly
Clark & McCormack
The Goodies
Burns & Allen
The Sklar Brothers
(AKA Derek and Clive)
The League of Gentlemen
The Firesign Theater
Groucho and Margaret Dumont?
Oh yeah! The Little Rascals
The Bowery Boys
The Gashouse kids
Akroyd and Belushi
Jack Lemmon and Walter Matthau
They were characters played first by two white men, then by two black men.
I’ll nominate the team’s creators, Freeman Gosden and Charles Correll.
No French & Saunders yet?
Andy Griffith and Don Knotts