Only fools isn't actually that funny, its just really well written and can turn average jokes into better ones because the characters are much better developed and charming.
One of my favorite British comedies that doesn't get anywhere near the praise it should do is Bottom. Watching Rik Mayall and Ade Edmondson in pure slap-stick is comical brilliance. Rik's expressions and the constant stupid but genious dialog between the two is belly aching stuff.
As for American things... they have some decent stuff, but I'm sure there is not a person on this forum who doesn't laugh out loud at Family Guy. Yes its a cartoon, but its probably the funniest thing out of the US for ages.