Patton Oswalt. Check out the routine from his Finest Hour (I think that’s what the show was called) special about walking his dog in New York City.
Gabriel Iglesias. Many Youtube videos.
My favourite British stand-ups (that haven’t already been mentioned) are:
Ricky Gervais - I guess you’ll probably have a good idea what to expect, but all his stand-up DVDs are worth watching.
Russell Brand - Don’t judge him on his mediocre US TV stuff, his earlier stand-up is worth watching
Al Murray “The Pub Landlord” - difficult to know if his character will travel well (he plays a certain stereotype of an extremely nationalistic pub owner), but has done so many good DVDs
Lee Mack - another comedian who does lots of one-liners. Very fast, very good timing.
Tim Vine [don’t worry puppets are not a regular feature of his act!] - probably the ultimate one-liner comedian, also does some very funny set pieces.
Billy Bailey - an accomplished musician, his best stuff is when he combines music.
US stand-up I don’t known much about. So I’d also be keen to get some recomendations I’ve watched some stuff on Netflix, but it’s hit and miss because most of them I know very little about. The best US stand-up I’ve watched recently is Doug Stanhope, I also liked Sarah Silverman and Demetri Martin (it must be said though that these 3 weren’t random picks).
Dennis Miller is one of my favorites.
I saw that insurance commecial, too! 
Second Eddie Izzard.
I second or whatever Kathleen Madigan - if you like Lewis Black you’ll probably like her. Also Christopher Titus and Ralphie May. Oh, and Comedian Bob Marley. That guys is hilarious.
Louis C.K.
Jim Gaffigan (Earlier stuff)
Aziz Ansari
Jerry Seinfeld (If you can find it. He’s brilliant.)
I’ve been listening to “I’m Telling You for the Last Time,” the past couple of days and I really had forgotten what a brilliant stand up he was.
Dylan Moran
My three favorites are:
Aziz Ansari
Katt Williams
Russell Brand
Or the original Ralphie May…John Pinnette
I’ve just come back from the Montreal Just for Laughs festival. Saw 17 comics in four days. If we knew more about the way things worked, we could have fit in even more. They hold it every July and I’d recommend it. Prepare to stand in long lines to get in early for general seating. But the theaters also all surround a perpetual street fair with a million things nightly. Hope that it’s not 90 and there’s no tornado, both of which happened earlier in July.
Some big names were disappointments. Sarah Silverman phoned it in so blatantly she may get an Android endorsement. Jimmy Carr is somebody I like a lot, but his material was much weaker than usual. Tig Notaro was trying to find a new post-cancer path and needs more time. You’ll probably see them all on Comedy Central, because it was taped for them.
My top three were all 30 or younger, so watch for them in the future, even though they’re hardly unknown today. All have huge upsides.
John Mulaney - SNL writer who does old-fashioned smart stand-up, part jokes and part stories. If you like John Oliver, then he’s a great alternative. He’s trying to launch a career separate from writing so you’ll probably see a lot of him in various settings and I wouldn’t be surprised if people saw him as an Oliver/Stewart successor. He’s clean cut! He’s a former cocaine abuser! He wears a suit! He’s got street cred!
Bo Burham - Made his splash at 20 so he has greatest hits already at 22. He does funny songs interspersed with jokes all set to a back-up tape timed to the millisecond that makes his act a meta version of meta. It’s all so perfect as to be slightly spooky. Broadway shows are sloppier. Every joke refers back on itself and every interaction with the audience is preplanned. Has fanatic fans that know every word, like rock groupies. He’s brilliant but has the drawback that he doesn’t project an actual personality. I don’t know where he goes from here. He probably has the next ten years already planned out.
Trevor Noah - I hate to push him because he’s going back to South Africa after spending two years touring the U.S. He’s the anti-Burnam, a quiet gentleman who is all personality and connects with the audience throughout an act that is otherwise just as precisely honed. (His best local line was that Montreal calls itself bilingual, but is really French with English subtitles. Perfect.) The whole hour is essentially one long story about his boyhood under apartheid and how he came to the U.S. so that he would have an identity: as black. The show’s called “Born a Crime” because he has a black mother and white father and interracial babies had no legal identity. And he does it all from a perspective of how happy his childhood was. The audience, more racially-diverse than at any other show, loved him, rightfully so. If the suits ever figure out what to do with him, he will be a gigantic global star, Will Smith before everybody started hating him.
All the big names speak in English, mostly because they’re nearly all American or British. If you speak French, then a zillion more shows open up. If you want certain types of comics, there was a dirty show, an ethnic show, a Britcom show, a nasty show, a Bar Mitzvah show, a new faces show. There were comic short films, an Off-JFL for smaller names, a Zoofest for weird performance art, and galas with big names introducing a squadron of slightly-less famous names. Prices aren’t outrageous, but costs will build up before you realize it the more you try to see. The website is - sorry - hahaha.com.
Most people only know him from his sitcom but I had the opportunity to see him live a few years ago and I found a whole new appreciation for his style of humor. Unfortunately his stand-up doesn’t seem to have much presence in the DVD/iTunes world.
I find Eddie Izzard hit or miss. When he hits he is one of the best. When he misses its a muddled mess. I can understand why when I heard about his process. Much of it is improvised. Of course he keeps the good bits and reuses them but he does all his writing on stage. His recorded stuff is pretty polished and funny but I’ve seen him doing live events and he isn’t always that good.
I saw part of his program on Showtime the other night, Trevor Noah: African American. I had never heard of him and only saw part of the show but I thought he was very good.
So last night I listened to bits and pieces of these comics:
Kathleen Madigan
Mitch Hedberg
Mike Birbiglia
Louis C.K.
Jim Breuer
Christopher Titus
And the only one I really ended up liking was Christopher Titus. Not that that’s a problem, that’s about the odds I expected (liking one comic for every 6 I try).
Kathleen Madigan has…something going on with her mouth or her accent which really distracts me. I mean I keep listening for it over and over again. Maybe in time I won’t hear it anymore.
Mitch, Mike, and Jim were both amusing, but Titus made me laugh out loud, and that’s what I am looking for.
Tonight I’ll try the next half-dozen. 
Thanks again!
If you find you like Trevor Noah, you might like South African Indian/Malay comic Riaad Moosa (or even if you don’t like Noah - you might actually relate to some of Moosa’s material better) - his standup is great, and he’s a good actor too (His film Material is quite good, and he’s going to be in Long Walk to Freedom, the Mandela biopic), and he doesn’t use profanity at all, which I didn’t even notice until it was pointed out to me.
UK comedians that I like are often regular QI and/or Mock The Week panelists (e.g. Jimmy Carr and Bill Bailey) I’d recommend getting hold of episodes of Mock The Week for a nice sampler of British stand-up, and then picking the ones you like and getting their own stuff .- Dara O’Briain, who hosts it, is awesome (his rant about the science in the movie 2012 is hilarious). I like Frankie Boyle best (warning - he’s a bit too much for some people, but if you like Jimmy Carr, you should be fine).
Not quite stand up, but David Mitchell’s rants in David Mitchell’s Soapbox webclips series are also worth checking out.
My two favourite British Stand Ups have very thick accents so you may struggle with them, but I like:
Ross Noble, a Geordie stream-of-consciousness weird tale-spinner. He likes owls and monkeys.
Dara O’Briain, an Irish comedian who jokes about nerdy things like video games and science, and occasionally Ireland. He talks very fast.
…and the more mainstream and intelligible:
Michael Mcintyre, who talks about middle class domestic life and ordinary everyday things.