So this is a Mt Rushmore. Which means that it has to be more significant than "I think that guy's really funny". It's more about someone who was significant in the craft or importance of stand-up as an art form.
It's like guitarists. Tons of people can play guitar like Jimi Hendrix, or Eddie Van Halen, or even Jack White. It's a matter of learning and practice. But they were creating new sounds, doing new things, which make them more important than someone who learns to play what they did before.
I look at Carlin and Pryor as not only supremely funny, but they helped redefine the entire world of stand-up.
On the above list you can take out certain ones who were "performers". Steve Martin is there. He was hilarious, but he was barely a stand-up. Andy Kaufman was bonkers, and funny, but it was performance art. Robin Williams was an absolute force on stage, but he wasn't necessarily a stand-up, he was just Robin Williams, a singular talent.
Hedberg, and Steven Wright (who isn't on this list but should be) were great, but not Rushmore great.
Lenny Bruce was before my time, so although I'm aware of his reputation, I know almost nothing of his actual comedy.
I look at guys like Norm MacDonald, Louis CK, and even Bill Hicks as great comedians, but not Rushmore.
I think you can make an argument for Eddie Murphy, Dave Chappelle, Jerry Seinfeld and Chris Rock.
My two:
- Seinfeld: First and foremost he is just a tremendous pure stand up comedian. But beyond that he was probably the pioneer--and much pilloried for it, i.e. "what--is the deal----with that?"-- of observational humor in stand up. And if you see him live, he is just polished and tight--even today. I saw him a few years ago in Vegas and he was 100% on top of his game.
- Eddie Murphy: I wonder what he would have been if he'd spent more time on stand-up than movies, but he was one of those who modernized stand-up and made it giant. He might have been one of the first "superstar" comedians, at least on TV.
I could see putting either Chappelle or Rock over Murphy, though.