I love Ernie Kovacs, he was a genius but his body of work is regretfully small. (same with Lenny Bruce or a John Belushi for that matter).
I think you have to choose Burns or Allen by the structure of the thread. But as a pair they were genius.
W.C. Fields I have never seen a single clip of his I found funny. Could you elaborate on when and why he was funny?
Jim
Good point, and I wish that Maltese would get mentioned more often - still, it’s when he and Jones were together that the real magic happened.
I like Mel Brooks. I really do. I have all the 2000-year-old-man books and albums. I actually went to the new Producers movie. I like The Twelve Chairs.
But Brooks’ is a one-note career that’s been going downhill for 30 years. He’s great at what he does, but he has no range. He couldn’t have played a straight part like Woody did in The Front. (And Woody’s been a voice actor too: remember Antz?) He couldn’t make any other kind of films but parodies. He doesn’t really write music, either: the way I’ve heard it is that he hums into a mike and somebody takes the basic tune and turns it into music. The Producers musical was structured by Broadway veteran Tom Meehan (whose humor collection, Yma, Ava; Yma, Abba; Yma, Oona; Yma, Ida; Yma, Aga…and Others, is one of the great forgotten works of modern humor).
Sorry. Brooks’ career is like a great spike of talent, but Woody’s is a vast plateau about as high. No contest. Chaplin is the real competitor.
Spike Milligan. The Goons were brilliant but pathbreakbreaking too. I doubt there could have The Beatles without Spike.
Peter Cook, although he never quite fulfilled his promise.
I don’t know if he qualifies as a comic genius, but Richard Pryor has made me laugh more than anyone mentioned so far, or anyone else that I can think of.
Peter Sellers
Steve Allen
George carlin
Marx Brothers
OK lets fight Three stooges-how they and no body else could have gotten away with what they did
Lewis Blacks last hbo standup may be the best ever
Woody Allen
Stan and Ollie
forgot Richard Pryor
Eddie Murphy had a time too
Well, we are talking “Comic Genius” and the last Woody film that was laugh out loud funny was long ago and is now very dated. If you want to argue that Woody is the better all around writer/director/actor I have to concede in a heartbeat. BTW: “Antz blew chunks” to use my nephews review. 
Jim
johnny carson
Scott Mclellan
Mel Brooks may be a “one-note” to some (like Woody Allen isn’t?) but he is one of the few to reach the top of the heap in TV, movies, Broadway and recorded comedy. By any objective standard he is one of the best. The problem is divorcing personal taste from the equation. Can it even be done? Woody Allen is a genius, but his comedy output has been sparse to non-existant the last few decades, and it was pretty monotonous before that. And what has Chaplin done the last few years?
Let me throw Steve Martin in there. Not just his satnd-up, but he has a distinguished movie career and even more imprssive may be the plays he has written.
Ah, but he did write, “What were you modeling, clay?” 
I can’t stand Brooks personally, and I think (perhaps because of what you noted - he does parody, period) that his stuff ages poorly, but I must defend the music thing. To me, that’s a valid way of composing. Yes, you should share credit with whoever can translate your hum onto paper, and fill it out against a chord scheme, but many, many people would be great composers but for that inability to come up with the interesting melody. And I think Chaplin “composed” pretty much the same way, so if Chaplin is Allen’s competitor for breadth of skill, you have to take his scores off the table (though he still has writer, director and actor).
I obviously don’t have any Schulz allies in this thread, but I’d like you to consider how odd and surreal it is - step back and consider as though for the first time - the idea of a little girl setting up a psychiatric booth. And how little we think of it to see Charlie Brown in unending therapy there.
Also, I’d like to paraphrase Sergio Aragones, who I think provides a good definition of greatness with the observation, “in 500 years, Schulz will be the only comic strip artist anyone can name.”
To back off performers and return to comic geniuses per se, S.J. Perelman would have to be close to the top. Not only was he crazy-hilarious in print, but he was part of the Marx Bros’. gag writing stable in their peak years of the early '30s.
For breadth of performance, Steve Martin. He has mastered goofy, deadpan, the banjo, weaves intellect into the goofy and makes it appeal to both high and lowbrow, can perform drama as well as comedy, and he can sing, tap dance and is also quite knowlegable about ancient Egypt.
For ability to asphyxiate within 15 minutes: Robin Williams. Also an accomplished dramatic actor. He picked up on personality transformation where Jonathan Winters left off.
Is there room in this thread for Monty Python? Or are we sticking with individuals? Eric? John? Michael? Graham? all pretty good on their own I guess, but as a unit–good God!
I was trying to make an ironic point.
And his character in Speak Easily is the poster boy for nebbish.
Gary Larson.
In a celebrity comedy death match, it would be Larson all the way. Except for the very end where Larson implodes in frustration at Schultz’ complete inability to grasp the depth of his irony.
Can’t call Martin a Genius, very good at times but not a genius. Robin is a great candidate, but I think he was funnier when he was still on coke.
Monty Python doesn’t qualify but might be a great spin-off thread.
Here it is: Greatest Comic Group of the Twentieth Century?
Jim
Chuck Jones was the greatest comedic genuis of the 20th century.
Legend has it that he did extensive experiments to figure out how long the pause should be between the time the Coyote disappears from sight after a long fall and before the audience hears the “splat” and sees the dust cloud. The answer? 11 frames. The man had humor down to a science.