Some British ones, since most of the American stuff has already been mentioned:
Red Dwarf
Black Books
The IT Crowd
The Brittas Empire
On seeing the OP, was going to say something similar. Unless you’re paying attention to each episode it could be very easy to lose track of what’s going on and you might not enjoy it as much as you really should. And even then it might take a couple of episodes to really get into it for some people.
I have already experienced this. During most shows, I will let it run for the few minutes I’m on the phone doing other things (btw, I’m an overnight EMD dispatcher for a private ambulance service), but for this first season of The Wire, I’ve found that I have to pause it while on the phone. No big deal.
Royal Pains starts up in a few weeks on June 3rd. It’s a great summer show, paired on Thursday on Burn Notice, I’d check out that block of awesomeness for some summer fun.
Freakazoid
Animaniacs
The Tick
Six Feet Under
Deadwood
Breaking Bad
British:
Sherlock Holmes (Jeremy Brett version)
Monarch of the Glenn
Coupling
Doc Martin
Cold Feet
Long Way Round (documentary series)
Monty Python’s Flying Circus
Canadian:
Trailer Park Boys
You really need Netflix.
Why Netflix, when I’ve got the Indianapolis public library!
Frasier
Daria
CSI (Las Vegas version)