I'm a huge comedy nerd, perhaps as important a part of my life as music and noise are.
So many favourites to list, some of which have already been mentioned.
Reeves and Mortimer are indeed sublime, and a definite key influence on the sense of humour I have now. A great example of well executed weird humour that managed to get into the mainstream. (a far cry from "lol random" utter shit like The Mighty Boosh)
The Simpsons was truly great obviously, anything before season 11 is well worth anyone's time I think. Never was anything so simultaneously popular and subversive. A real shame that it's become the sort of mediocrity it used to lampoon so expertly and ruthlessly. I've heard criticisms of most of the episodes having happy endings, which of course would be required for a prime time family orientated sitcom, but they always had some cynical bent to them, such as Homer crying at his children "both being losers" when they decide to call it a tie in a hockey game, or again Homer declaring he'd learned nothing from media lying when asked if he'd learnt a lesson from being falsely portrayed as a sex offender on TV.
When it comes to stand up I used to favour US stuff, but I've come round more to UK stand up comedy in recent years. Obviously, like in any country, the majority of it is useless crap, especially the more mainstream stuff, but comedians like Stewart Lee, Daniel Kitson, Simon Munnery and Jerry Sadowitz manage to deliver material both substantial and hilarious, that rewards re-visitation.
US comedy unit PFFR are possibly my favourite comedy people ever, everything they have produced is totally brilliant. Clearly some influence from UK innovators like Chris Morris but taken much further into some truly head scrambling genius. Xavier:Renegade Angel manages to be both flippant and profound, mocking new age overanalysis, yet warranting thorough analysis as it is totally dense with brilliant jokes and writing, and presented in a wilfully alienating style to put off those who aren't willing to look beyond the deliberately hideous visual style and ridiculously fast pace. Wonder Showzen is endlessly creative and funny, one of the most bitter and savage satires imaginable. Delocated is the most "accessible" show they've made perhaps, full of very low brow silliness that in the wrong hands would be simply cringe worthy. But it is brilliantly performed and written, packed with the trademark PFFR meta humour taken to insane heights. The Heart She Holler is a shamelessly gruesome gothic soap opera, which I can imagine appealing highly to fans of melodramatic trash auteurs such as John Waters and George Kuchar. Shades of the most disturbing elements of Twin Peaks abound as well, but done in a really camp and casual way. PFFR rule!
A lot of Adult Swim shows I find do unfortunately fit into the aforementioned "lol random" category but they've made some really great stuff too. Of Tim & Eric produced material I enjoy Check It Out! With Dr Steve Brule the most, wonderfully wrong late night hazy atmosphere to that one. The Eric Andre show is amazing as far as newer comedy goes, similarly brilliant late night public access TV feel to it.
Nathan For You is another recent one I've found highly appealing, very original concept and fantastically played. The best "reality" comedy I've seen, the presenters deadpan aspergic delivery fitting the material perfectly.
I'm missing out on a ton but that's enough to be getting on with.