Even though I don’t speak Chinese, Stephen Chow and Ng Man-Tat are the funniest pair of guys I’ve ever seen.
Adolph Hitler and Josef Stalin’s “Who’s being gassed on first” was one of the funniest bits I’ve ever heard.
Right up there with Mao Tse Tung and Lenin’s “Dead Parrot and Everyone who disagrees with me is dead too” sketch.
They were great individually, but their only teaming (My Little Chickadee) was a huge disappointment.
Oh! Nearly forgot Gallagher and Shean, Smith and Dale, and The Happiness Boys (Billy Jones and Ernie Hare)!
looks at location 
Did their fame spread to NC or are you an ex-pat?
Have to go with Stan and Olie.
Jerry Jones and Barry Switzer
He used to be on The Hudson Brothers show when I was a kid up in Ohio back in the 70’s…
Still cracks me up thinking about it…
I’m gonna be different and say Tim Conway and Harvey Korman. These two are hilarious. Their bits never fail to completely crack me up.
Probably not in the top ten, but I always found Burns and Schriber to be hilarious. Marx Brothers are high up on the list, Laurel and Hardy, Burns and Allen, Nichols and May, Bob Newhart and a telephone.
Bob Williams and his dog Louie. Funniest animal act I’ve ever seen. (“Heeeee’s thinkin’ about it!”)
As for all-human teams, I agree with a couple of the ones already mentioned:
Mike Nichols & Elaine May
George Burns & Gracie Allen.
Marx Brothers. Head and shoulders above everyone else.
Monty Python as second place.
If you ever get a chance, go see the Reduced Shakespeare Company. Their shows are as close as those of us living today will ever get to seeing the Marx Brothers live on Broadway.
Abbott and Costello’s “Who’s on First” routine may be the single funniest bit ever done, though. It’s an absolute miracle of timing and inflection.
I was going to mention Conway and Korman along with Carol Burnett and Vickie Lawrence as a complete set. Although I will agree that Conway and Korman were a great pair. It wasn’t a good piece unless Tim could get Harvey off his game. They were a riot.
The gang on Rowan and Martins Laugh-In were good too. They got yanked to early IMHO.
Oh, man. I had to rush back to the keyboard because I couldn’t believe I forgot about these guys:
For you younger Dopers who don’t remember the 60s, they had a radio show in L.A. but were best known for their incredible conceptual comedy albums, How Can You Be In Two Places At Once When You’re Not Anywhere At All? (introducing Nick Danger), and Don’t Crush That Dwarf, Hand Me the Pliers, the best record album of all time.
There was never anybody else like them, including their later selves, but at their best they could compete with any comedy troupe anywhere anytime.
I gotta disagree. That movie is my favorite Mae West film and second on my list of best W.C. Fields flicks.
And another vote for The Three Stooges.
How about another W.C. Fields team up. He made a great foil to Charlie McCarthy (since Edgar Bergan/Charlie McCarthy can’t REALLY be called a team an their own). I agree with most of the others already listed (they are good for sound clips, but I’ve never really liked the Stooges).
I couldn’t exactly call them the greatest, but The Times Square Two never failed to make me laugh.
I’d like to mention the “Higgins Boys and Greuber” or however his name was spelled. For a long time the funniest thing on “The Comedy Channel.”
Great call Exapno. “Shakespeare’s Lost Comedie” is on my funniest of all time list.
My Top Ten , in no particular order
Marx Brothers
Bob & Ray
The (various) Three Stooges
Peter Cook and Dudley Moore
Burns and Schreiber
Stiller and Meara
Smothers Brothers
Sid Ceasar and Imogene Coca
Can I count Andy Griffith and Don Knotts?
Nobody mentioned Franken & Davis yet?
The Two Ronnies
and I loved the Firesign Theatre, too. Also Harvey Korman and Tim Conway…well, the whole cast of the Carol Burnett show were so funny together that sometimes you could just tell that they were cracking each OTHER up so badly they could hardly get through the sketch.
Morecambe and Wise…without a doubt:D 
Burns and Allen, Bob and David, Cheech and Chong.