I absolutely love stand-up, I practically devour it almost on a daily basis and honestly didn't think anyone here was really into stand-up that much. Great suggestions have been already made, it all depends on if you want to check out current greats or stand-up classics. In the classics then definitely check out Carlin, Bill Cosby, Richard Pryor, Eddie Murphy and Jerry Seinfield (some off the top of my head). I love a wide variety of comics (some popular some not) I strongly suggest check out:
Dave Chappelle, Mike Birbiglia, Louis C.K., Nick Swardson, Doug Benson, Anthony Jeselnik, Aziz Ansari, Bill Burr, Bo Burnham, Brian Regan, Daniel Tosh (I honestly find him hilarious), Gabriel Iglesias, Jim Gaffigan, John Mulaney, Kevin Hart, the only Kevin James stand-up (Don't Sweat the Small Stuff), Kyle Kinane, Lewis Black, Mindy Kaling's stand-up on youtube, Nick Thune, Patton Oswalt, Steve Bryne, Whitney Cummings, Sklar Brothers, Rory Scovel, Donald Glover, Tom Segura, Natasha Leggero, David Cross, Illza Shlesinger...... I'll stop I know that's a lot I kinda just unloaded any comic that I knew that I liked.........
As a side note if anyone is interested Doug Benson's podcast "Doug Loves Movies" is hilarious and has all types of guests ranging from actors to comics such as Jon Hamm, Ellen Page, some of the comics listed above, Sarah Silverman, John Lithgow so on and so on. I suggest give it a try it's really funny in my opinion and you can find it for free on iTunes or google Doug Loves Movies