I’ll chip in with Stewart Lee.
Perhaps an acquired taste and better in half hour sections than quickfire routine but he is always interesting.
Maria Bamford
and I second
Eddie Izzard
Mitch Hedberg
Dave Attell
Brian Regan
I mentioned a couple favorites upthread that I’ve seen in person. However, the greatest stand-up performance I’ve ever seen, on DVD or otherwise, is Bill Cosby’s Himself. Nonstop hilarity.
QFT.
Hey, a commercial just came on my TV telling me that Keifer Sutherland is on Broadway in That Championship Season. Jason Patric, Brian Cox and Chris Noth also were featured in the commercial. And then it (briefly) mentioned that it also starred Jim Gaffigan.
I also wanted to second Giraldo, Atell and Hedberg. Also that guy who I cannot remember his name. He sometimes travels with Foxworthy and The Cable Guy but he’s not anything like them. Chomps a cigar and drinks heavily. Gah! I can’t remember his name!
Ron White 
Ron White.
Thank you!
I’m going to continue to try to pimp Kyle Kinane, whose career seems to be taking off now. His album Death of the Party is very, very funny. He did a short Comedy Central special recently and was on John Oliver’s standup show. That’s not a lot of material but what there is is very good. I think you’d like him if you like Louis C.K.
Thanks for the replies! I am checking them all out.
Dave Chappelle is my long-standing favorite…he’s got the greatest delivery I’ve ever heard. Watch his entire Killin Them Softly show, from 2000 (links to the other parts in the sidebar).
Another guy I love, with a very different style, is Stewart Lee.
Russell Peters. I’ve been a fan for years (and just saw him at Casino Rama this past weekend).
And I’ll throw my hat in for Jim Gaffigan. Saw him in Toronto a few years ago, and I literally had to take hold of myself and stop for a minute. I thought I was going to pass out I was laughing so hard.
Josh Blue is awesome! One of my all time favorites for sure.
Another vote for Eddie Izzard, as well.
Funniest I’ve ever seen was Rodney Carrington.
Sean Lock. Omid Djalili. Jack Dee. Bill Bailey. Dara O’Briain. Jasper Carrott. One of each:
I think the Dara O’Briain one will go down well here.
Also Frankie Boyle, but I don’t think I’ll link to him.
I’ll second most of the names mentioned upthread, and add Dylan Moran. I have to say, he’s my all-time favorite out of the lot.
This is a long shot, but I wonder. I like all these guys, and I also like, of all people, Kathy Griffin. Check her out–I’m curious if I’m as strange as I think.
If you do like her, try Joel McHale, too.
He did say Bill Hicks already…
Oh, and to add to the list, besides the already mentioned Eddie Izzard, check out Mitch Hedberg. The guy was a great joke writer, don’t let the stoner delivery fool you.
Look for Anthony Jesselnik. He killed at the Trump Roast.