A type of show that exists in the UK but not in Canada is what I've heard called "quiz comedies" (or "quizcoms" as one channel, Dave, has abbreviated it as). Essentially, these quiz shows are as much quiz shows as Who's Line Is It Anyway? was a game show - they follow vaguely the format by having contestants who answer questions, but the focus is really on comedy and not on the contest (as Drew Carey put it in the American-version of Who's Line Is It Anyway?, "the points don't matter"). In fact, some of the quiz comedies were created by Dan Patterson, the same guy responsible for Who's Line.
Why I mention this is that many of these shows are quite funny, becoming some of my favourite shows over here.
The shows that I'll describe below are orignally produced by BBC and Channel Four, but I've been watching them in re-runs on the afore-mentioned channel Dave ("the home of witty banter" according to their slogan), which was running them every week night all in one go. There's video clips at the websites of most of these shows, so you can check them out if you so wish (and since writing about comedy is sort of fruitless and impossible, I really suggest the clips over my descriptions).
QI (Quite Interesting) is a quiz show hosted by Stephen Fry that has 4 contestants, generally comedic personalities. Alan Davis seems to be on it perpetually as as contestant, generally losing. The questions are quite difficult and obscure, so giving a wrong but interesting answer is encouraged, or just discussing the question. Points are deducted for giving incorrect answers that are commonly believed to be true (for example, answering that "Ring Around the Rosie" is about the Black Death was one of them). It basically ends up being a reasonably intelligent conversation peppered by jokes, so it's quite enjoyable (and unusual for television).
Have I Got News For You has a celebrity host who cracks jokes about the news of the week, and quizzes two teams on the news. The captain of each team is constant from week-to-week (being Ian Hislop and Paul Merton) and is joined by a celebrity guest, generally a comedian. Like QI, questions result in panelists satarizing the news.Mock The Week is sort of a spin-off from Have I Got News For You, but is more improvisational political sketch comedy than quiz show. The host is Dara O Briain (that's Irish, being pronounced something like "dahra oh-bree-an"), and there's 3-4 regulars and comedian guests to add up to two teams of three each. A few of the sketches aren't hilariously funny, but the banter between regulars and the rapid-fire segments makes up for it. I particularly enjoy the aforementioned host O Briain, Frankie Boyle, and Hugh Dennis.
Never Mind The Buzzcocks (doesn't seem to have its own page so that's the Wikipedia one) is a quiz about the music industry, with varying hosts over the years and two regular team captains, Phil Jupitus and Bill Bailey, who each have two music-industry guests on their teams. There are quiz rounds that involve music itself, like finishing-off lyrics and guessing songs based on versions performed by team members, but some of the questions are almost designed as ways to make fun of pop musicians, like asking what strange items stars demand to have backstage, or who flew his hat first-class across Europe to a charity concert. Bascially, they just mock pop music.
Watching these shows has introduced me to many new comedians and allowed me to see more of comedians I'd only caught snippets of back in Canada. The two news-oriented programs have also had the benefit of teaching me about the politics and recent history of the UK. I first learned about politics by listening to the Royal Canadian Air Farce on the radio with Dad when I was a kid, and I've learned much about US politics from watching The Daily Show with Jon Stewart and The Colbert Report, so I've just carried on that method over here. It's more fun learning that way.
I'm branching out in my comedy viewings now, having started watching Chewin' The Fat, a Glaswegian sketch comedy, on DVD and so far it's very funny. The DVD actually comes with subtitles as an option for those who can't understand the patter, but so far I'm getting on right enough without them.