Eugene Mirman: He's got an absurdist style. He just put out a CD on subpop, so you can probably find sample tracks at subpop.com.
Demetri Martin: Probably going to be pretty huge soon. He has some sort of a cross promotional endorsement deal with Microsoft and Comedy Central. He's sorta like Steven Wright, except younger, hipper, and also he has hair.
Aziz Ansari: Another hip comedian. I heard he was shooting a pilot for MTV. His delivery reminds me of Mitch Hedberg, except faster and higher pitched. Like if you played a Mitch Hedberg record at the wrong speed. But some people disagree with that. And his jokes aren't really Mitch-like at all. But he's really good, especially considering that he's only about 23.
Andy Milonakis: He actually has his own sketch comedy show on MTV. He's going to be starring in a remake of Ferris Beuller's Day Off that will probably make his career. Also, I'm not sure if the deal has actually been signed yet, but he's supposed to be playing one of the two Michael Meyers roles in the next Halloween.
My favorite comic to see live is Paul F. Tompkins, but he's famous enough that you're likely to have heard of him. Same for Jim Gaffigan, Louis CK, Jimmy Pardo, Doug Benson and Andy Kindler.
Also, I live in Austin, and the best local comic by far is a guy named Brendon Walsh. I think he's started going on the road, and he's well worth seeing.