Three more nominees:
David Foster Wallace
Neil Stephenson
Phillip Roth
(nit) - the feud is with Updike, Mailer and Irving. Wolfe respect and likes Roth.
Having said that, I couldn’t agree with you more, Exapno - Wolfe doesn’t hold a candle as a novelist to most of the names listed in the thread. He is an interesting journalist - especially when taken within the context of his time and what he did to influence journalistic style. I still love The Electric Kool-Aid Acid Test as a piece of non-fiction reportage.
But as a writer, as in fiction? Not even close. Not even worth considering.
When Roth can write American Sabbath, the Human Stain, I Married a Communist and his latest book - all in his 60’s, and all critical and commercial successes - is there any question that he is the dean of active American writers?
Richard Ford, anyone?
I always thought that he writes like a graduate student trying too hard. I don’t think he’s talented enough; or if he is, he sure hasn’t learned to wield that talent well.
I second (or third) Irving–although I think his best work has already been written.
As much as I like David Foster Wallace, I don’t think he has enough of a body of work to judge whether he’s in the running for greatest current American writer. Phillip Roth, Norman Mailer, Don DeLillo, John Updike, Thomas Pynchon, and John Irving certainly do. My vote’s with Roth, although I think the “greatest current American writer” nomenclature’s a pretty useless thing in itself.
I can’t believe I forgot to mention E.L. Doctorow.
But I agree with what several other posters have said, that if you had to give the title to any one writer, it would be Phillip Roth.
I’m still surprised that Irving is getting mentioned so many times - I thoroughly enjoy most of his work (Widow for One Year excepted), but I just have never thought of him as “great”, and didn’t think he was generally regarded as such.
I’ll 2nd that. He has an expansive body of work that has been both widely acclaimed and dismissed due to where it’s found in most bookstores - the SF&F aisle. DeLillo writes prettier sentences, but Wolfe tells better stories.
What’s this obsession with the greatest this and that? They’re all (arguably) great writers. There’s no number one, objectively speaking.
One of my definitions of “greatest writer” is the one who packs the most fun into the fewest words. On that standard, and limiting my choices to book-length writers, I nominate Carl Hiaasen, with a Lifetime Achievement Award for Elmore Leonard. 
I’ll agree with the premise that Tom Wolfe is among the “greats” – I refuse to say “greatest” because I haven’t read even a fraction of the “important” works of this century. I’ll also put John Irving in there, and Kurt Vonnegut, although each of the latter suffer from style repetition in their later works. I’ll say that “Infinite Jest” was good enough that Wallace will still be known (if only for that one work) for a long time to come. Neal Stephenson, despite the Baroque Cycle, still basically writes fiction that serves as entertainment – not as a stimulus for debate, or to provoke thought or emotion – and so as good as he is at his craft, his importance to anything other than the expected quality of entertaining fiction will sadly be minimal. Likewise Orson Scott Card, except that he may be remembered for Ender’s Game provided he’s not still writing sequels and prequels that dilute it when he should be resting on his damned fine laurels.
Horrible horrible book!
The person who reviewed the new book for Newsweek* didn’t like it, but the review was so vehement, I suspect maybe they know each other.
My vote goes to Don Robertson, for The Ideal Genuine Man, Paradise Falls, and his Civil War trilogy. I haven’t read his other books yet, but the people who gave them to me and said “You have to read this man!” They were right about the first four, so I’m thinking the rest of them will be just as good.
I like Gene Wolfe too (what an imagination he has) but I think the other writers mentioned here (Roth, Updike, Morrison, Ford, etc.) will be read a hundred years from now and will do a better job of conveying all the different truths of 20th century American culture. I don’t think Thomas Wolfe is in the same league. (I’ve only read Bonfire.)
Damn. Can’t code. Can’t even count. 
Is this thread arguably the most pointless thread started on the SD this week?
Tom Wolfe. Never Thomas Wolfe. Yet another different Wolfe entirely. Nor is he Tobias Wolff. Who wasn’t the one who wrote about Nero Wolfe.
Wolf Blitzer is a different mammal altogether.
I thought the Newsweek review was surprisingly mild. It’s not as harsh as Michiko Kakutani’s in
The New York Times but makes exactly the same point. Wolfe relies on lots of detailed reporting to try to set a scene, but the details aren’t convincing and he fails to create characters.
Dang it, if the board would let me go home again, I could have edited the third mistake in my post.
I give up.
I’ll take Richard Russo and Kent Haruf above the others mentioned, but they’re all quite swell.
Oh, in light of that definition, I offer up Tom Robbins. That man turns a phrase like no other.