I have to say that I love almost all British comedy,especially the oolder classics such as Monty Python's Flying Circus,Benny Hill, Julian Clary,Vicar of Dibley,Fawlty Towers,As Time Goes By,The Good Life,To the Manor Born,Yes Minister, etc etc etc!!!! The more recent My Family,Little Britain,and suchlike are also super!! Aussie shows which are not technically Comedy,but wuich m ake me laugh out loud are Spicks and Specks, and The Gruen Factor! I also get a giggle from Dirty Laundry! I love ant shows which make me laugh out loud!
I'd have to agree & go mainly British, too - with: My family; Worst Week of my Life,Vicar of Dibley, The Young Ones, The Good Life, Outnumbered, Bread, Black Books. Best of these being 'The Good Life', by dint of the fact that it was ahead of it's time; then 'My Family' for sure, for it's irreverent look at British, middle class family life. American? Definitely 'Ben & Kate', for it's look at another sort of middle class modern family, Sadly cancelled after just one season. Australian? Have to be 'Offspring', for a look at an Australian, middle class, somewhat dysfunctional? modern family, with all the hiccups. Trumps 'Offspring', for local comedy that's new, vibrant and Australia's answer to Bridget Jones, in Nina as the main character. And for an awesome title track and sequences. The new American sitcom: 'Mom', has it's moments at times too.
UK's 'Not Only, But Also' with the best comedians' ever, Peter Cook & Dudley Moore. Cook was pure genius. Moore was one of the best Jazz musicians, piano, I've ever heard! Sadly, they're no longer with us.........
I loved/love all the UK comedy shows. I didn't like the US ones, except for Family Ties & Everybody Loves Raymond. (I really disliked, Mash & Hogan's Heroes but the question didn't ask, what I didn't like!)