QI is fantastic - and all the episodes are up on YouTube. It's ostensibly a quiz show but it's more just plain comedy.
Have I Got News For You is a topical quiz show - recorded on the Thursday, shown on the Friday - about the past week's news. Again, the quiz element is almost non existant. A lot of it is based around either improv comedy skills or satire and it tends to be very, very funny. Some on YouTube.
Doctor Who is fantastic if you like SciFi. It's a British take on an American big-budget scifi show. It's great (if a little too obvious by one writer in their trying-to-copy-Joss-Whedon's-style).
I will think of some more later.