I definitely prefer British humour to American humour. I found the British version of The Office to be much funnier than the American version which I found lacking in bite compared to the original.
Black Adder is a good example of Brit humour. It is, IMO, the most hilarious show ever made and A Black Adder's Christmas Carol is one thing I must watch around Christmastime. But it's basically horrible people saying and doing horrible things and then dying at the end of the series. It's witty, dark, and sarcastic, and a far cry from typical goofy American comedies. I've tried introducing people to it, but half of them don't get it and think it's just cruel and depressing. I think that's one of the main differences between American and British humour- British humour isn't afraid to have main characters that are unlikeable. Take Basil Fawlty for instance. In an American comedy, he would just be a clueless goof that has bad things happen to him and his hotel. That way, we would be able to sympathize and root for him. But he's not. He's rude, bitter, and just all around not a nice guy. In fact, none of the characters in Fawlty Towers are all that likeable but the show is still enormously funny. My Family is the same, most of the characters are unlikeable or at best annoying. It's not a lovey-dovey family comedy where they all hug at the end of each episode having solved the problem at hand.
Coupling is also fantastic but waayyyy too racy for American TV. Honestly, who thought that would work ? Steve's speech about Lesbian Spank Inferno? The trip to the sex shop to buy "Junior Patrick", which was then given to Steve's mother-in-law? A whole two episodes on The Melty Man? Even the whole thing about checking Susan's remote controls for batteries. Characters on American sitcoms just don't talk about these things, unless it's Sex and the City on HBO.
A great American black comedy from recent years is Thank You for Smoking but I believe it was largely unsuccessful, which is a shame because it's great. Not surprising though, since it also doesn't have a clear good guy to root for, with all the characters rather, err... morally ambiguous.