All the greats have been mentioned so I'll give a shout out to Jeff Ross for owning roasts for about 20 years now.
Chappelle definitely still has it. He came to the Netherlands last year and he killed it. Made some awesome cultural reference jokes like this racist version of Santa Claus we have here, red light district and such. He even dissed his body guards for looking like sissies (they have no guns obviously and are in general not as big as some of those huge dudes from the US) and asked some questions to the audience and just roasted them. Lastly when the lights guy didn't follow him fast enough he started running across stage to see if he could catch up and acted as the guy like "This N*** won't stand still, damnit". Hilarious!!
From a standup perspective: Louis CK. I like Chris Rock, but he only did like 2 standup specials since 2000 with "Never Scared" and "Kill The Messenger". Chapelle Show was great, but then he went MIA for like a decade. I saw his Netflix specials but I don't think it was as good as "Killin' Them Softly". Louis CK has done 10 specials since 2000. Yeah, he's done some TV shows and directed films, but standup is his bread and butter. And I don't think he can be matched on stage. Special nod to John Mulaney. He'd be a candidate for 2010-2030.
Is there a definitive Mulaney set I should watch? I’ve seen one of his specials and didn’t love it. Killing them softly is one of the best specials ever put together. Dave doesn’t have to hit that level again to still be amazing. His stuff is still as good as it gets in modern comedy. Louis CK’s volume and high level of consistency probably makes him the best of the 2000’s.
Dave Chappelle for the first 10 years. His last special wasn't nearly as good. These days, I love Bill Burr.
Twenty years is just too long a range to name a single best, where a comedian's trend during this time period especially is about their show gets super hot and they knock a few specials out of the park, and peak hard over a few years. We're either just naming our favorites, or who's hottest lately. Repeat what others have said, chapelle, gaffigan, mulaney, louis ck, bill burr, but if I had to pick one, sticking with Jerry Seinfeld, even though his best days predate 00-20 obviously, his shows domination & standup, but he still has late material in cars & coffee & an occasional special. Also depends on how tightly you define what comedy means to you- Seinfeld & mulany are straight forward and just about the jokes, writing and delivery, talk show performances. Whether how clever or original a bit is matters to you. Because I have to admit Chapelle has made me laugh harder at more stuff in this time frame, but no longer, as he & his act has not aged well to my eyes vs. when he was skinny & young, could visually punctuate with expression, never realized how much that was helping him before.
I'm gonna have to check out Fat Dave, don't think I've seen any of his recent standup. Has anyone seen "Crashing" with Pete Holmes? I had no idea who Pete Holmes was, but the first season was pretty good (if you like stand up you'll like it). Mulaney and a bunch of other guys make appearances. Speaking of Mulaney, was talking about this with my brother a couple of nights ago, he'd just got back from seeing Eddie Izzard, but he told me to watch this snl clip with Mulaney: