Do you want to cover everything? stand up and comedy acting in movies & TV?
There's a lot of choices from the people that came up through Vaudeville & Burlesque, then into TV as it evolved:
Harold Lloyd
Buster Keaton
Marx Brothers, Groucho in particular
Three Stooges
Ritz Brothers
Milton Berle
Jackie Gleason
Lucy Ball
Phil Silvers
Sid Caesar
Jonathan Winters
Ernie Kovacs
Steve Allen
Jimmy Durante
Danny Kaye
Bob Hope
Carol Burnett
Johnny Carson
Shecky Greene
Danny Thomas
Jerry Lewis
Dean Martin
and later
Smothers Brothers
Flip Wilson
Richard Pryor
George Carlin
If you just want stand up in the last 20 years I'd say Gallagher.
Good list knowone.
Although you are missing Red Skelton for U.S. TV themed comedians. Bill Cosby, Joan Rivers, Alan King, Martin Mull, Jerry Stiller and Ann Meara too in the US market as well.
And Dudley Moore, and Peter Cook for U.K. based TV. Benny Hill is also in that category.
Comedic Troupes...
Monty Python
Laugh In
Second City Television
Saturday Night Live
The Kids In the Hall
As for sitcom comedians leading to films ...
Flip Wilson
Bill Murray
Dan Ackroydt
John Belushi
Steve Martin
John Candy
Chevy Chase
Rick Moranis
Dave Thomas
Jerry Steinfeld
Michael Richards
Rich Hall
The Smothers Brothers
Comedic writers and funny in their own right...
Mel Brooks
Buck Henry
Marty Feldman
Tim Conway
Harvey Korman
Then finally the standup comedians...
George Carlin
Richard Pryor
Robin Williams
Rodney Dangerfield
Eddie Murray