This era can be loosely defined as from now to five years ago. I’ll start the proverbial ball rolling:
From this era:
Sasha Baron Cohen
Larry David (a holdover from Seinfeld days)
Jack Black (for his work with Tenacious D)
Of All Time:
Eddie Murphy (Re: SNL, 48 Hours and “Donkey” from “Shrek”)
Richard Pryor
Bill Murray
There are some others who come to mind, but I haven’t watched them enough to be worthy of identifying them.
Question: does Jon Stewart belong on either list?
Currently
Stephen Colbert (I think Jon Stewart is more of a semi-serious newsman, however poorly that reflects on journalism.)
Seth McFarlane (I’m not a huge fan of his shows, but I have to admit there’s something to their popularity, even if it isn’t my style.)
All-Time
Groucho Marx
Mel Brooks
Gene Wilder
All Time:
Charlie Chaplin
Buster Keaton
W.C. Fields
Jacques Tati
Woody Allen
Mike Nichols and Elaine May
Monty Python’s Flying Circus
Currently
Ricky Gervais
Zach Galifianakis
Current:
Eddie Izzard
Russell Brand
All time:
Eddie Izzard
Mel Brooks
Stephen Wright
All Time:
Will Rogers - the original John Stewart
Abbot and Costello - Nailed the buddy schtick
Marx Bros - The great ensemble comedy, funny at multiple levels
Stooges - perfected physical comedy
Lenny Bruce - made it funny to be crude
George Carlin - Took Lenny’s work further
Today?
Stewart / Colbert are my favorite.
I knew someone had to mention Ricky Gervais - Yes I enjoyed The Office but that guy is the most over rated “genuis” ever. And his stand up is awful.
anyway I will mention laurel. & Hardy
I’ll ditto Gervais :). Especially for Extras.
Current: Larry David, for taking Jewish humor to it’s supreme height, with all beauty of improvisation.
Stephen Colbert, for folding over reality in character.
Amy Sedaris, for being a foible to what’s supposed to be femme cutesy, wicked good with the truth.
I don’t know enough about current comedians to comment, so I’ll stick with the classics:
Groucho (first, then the rest of the Marxes)
WC Fields
Mel Brooks
Carl Reiner
Allan Sherman
Bill Cosby
George Carlin
Steve Allen (more of an all-around entertainer, but still)
Henny Youngman
Monty Python
(Irretrievably balanced toward Jewish humor. Whattya gonna do?)
Kanye West is the best comedic genius of all time, ALL TIME!
*That meme is probably old but I don’t care, it’s still funny.
Stephen Fry
Simon Pegg
Bill Bailey
Bob Newhart doesn’t get enough credit.
Two huge hit television shows, some of the highest selling comedy records of all time and a completely unique comedic persona.
I <heart> Bob Newhart.
Well, under “all time,” it couldn’t be Mark Twain. His twin brother might count, though, as the one who survived that childhood bathtub drowning incident. According to Mark Twain.
Current:
Will Ferrell. I think he can pretty much do no wrong. I hope he starts extending himself somewhat beyond his current character type, as Adam Sandler has done (with surprising success).
Bill Murray. He’s always funny in the most satisfying way even when he’s being serious. Groundhog Day is my vote for the best comedy of all time, and its success depends almost entirely on Murray’s performance.
Jake Johannsen. Sure, he’s basically unknown, but I’ve never seen standup that can compare. Check him out on YouTube, here’s a sample.
Danny Kaye
Today: Brian Regan, Larry David, Jake Johannsen, Jim Gaffigan, Amy Sedaris.
All Time: W.C. Field
Groucho!
and Bill Hicks 
Laurel and Hardy
Carlin
Mel Brooks
Monty Python
Peter Sellers
The creators of Rocky and Bullwinkle Show
Beluchi
My favorite comedian is Patton Oswalt. I think he’s fucking hilarious and ideologically I generally agree with him (I’m not talking about politics, he’s not really political, I mean his outlook on life and how people are.) Bob Odenkirk and David Cross, also amazing. I’m a huge Ricky Gervais fan. I think Steve Carell has also proven himself to be a great comic talent.
So that would be my list of the comedic geniuses from this era: Patton Oswalt for standup, Bob and David and Ricky Gervais for TV, and Steve Carell for film.
Andy Kaufman