It's already been said, but it can't be said often enough.....or loud enough........
(the new) <blink>Battlestar Galactica</blink>
Be sure to start from the *very beginning* of the new Battlestar Galactica, with the miniseries (the season 1 DVDs come with it if I'm not mistaken). Like someone else said, it's best to approach it like a book. It's one big story.
After that, there are a few others that are good as well. Onodrim mentioned a lot of great shows, but it can be hard to tell what the "good" vs "great" ones in her list are. So, here are my recommendations (for AFTER the new Battlestar Galactica

)....
I'm going to start out with a British show, since you've already displayed an interest in British television with Footballers' Wives and The Office (UK): check out
Life on Mars. Honestly, I'd be surprised if you can find it on DVD in the states, but keep an eye out. The second (and last) season is about to start and the first season was only 8 episodes, so there's not much dedication involved in watching it. That said, it's a great show. The basic premise is that a police officer from 2006 is hit by a car (while he listens to the song "Life on Mars" by David Bowie, hence the name of the show), and wakes up to find himself in the 1970s. He's still a police officer in this time period, but his rank is a bit lower, and he's obviously not sure what the hell happened. Neither are you. Was he thrust back in time? Is he in a coma? Is he dead? Is this a new twist on Quantum Leap? The show
could be just another police drama set in the 1970's, except Sam (I shit you not, his name is Sam, I'm not making a joke about Quantum Leap here

) is initially thrust right into a case that's directly related - 30 years earlier - to the case he was working on in 2006. Is he really in the past? Is he making this case up in his head? The latter question seems quite possible, because Sam also occasionally hears strange sounds that no one else around him hears. Sounds like the beeping of hospital machines, doctors talking about him, etc. One of my favorite early scenes involves him sitting in his apartment at night with the TV on, and the math instructor on the TV suddenly starts talking about "the patient"...only to revert back to math shortly afterwards. It's done REALLY WELL. Anyway, if you can't tell, I think it's a great show. One of the better concepts and shows I've seen in recent times in fact. If you see it around, check it out.
Keeping with the more "serious" shows, you may want to check out both
Rome and
Carnivŕle. Both are very well-regarded shows, although I must admit I haven't seen too much of them. They are high up there on my "too see" list.
Taking a turn for the less serious,
Dexter is also great. Creative and fun, what's not to like about a socially inept serial killer who works for the police?!
Following Dexter, I'd suggest
Nip/Tuck which is mostly absurd, with some serious occasionally thrown in. For a show which intentionally pushes the envelope, it has racked up a formidable list of controversial issues addressed, including organ harvesting, pedophilia, incest, necrophilia, zoophilia, sadism, swinging, orgies, bisexuality, teen threesomes, transsexualism and transvestitism, christian science, scientology....well, you get the idea. The list goes on. Needless to say, the show is a lot of fun
Moving more towards the "popcorn" shows, as
JustJess called them, we've got
House, M.D. and
Boston Legal. House is a decent medical show made great by Hugh Laurie. Don't get me wrong, I don't think the parts without him are bad, it's just that he and his character are what make the show stand out. This issue has been covered well enough for this thread. Boston Legal is, again, a show which aims to be absurd a lot of the time, and it's great at accomplishing it with the William Shatner/James Spader duo.
Those are my main recommendations. A lot of the other shows mentioned are great shows, but I know how much it can suck when you ask for recommendations and you get a list which is 30 items long

If you're looking for some more British television,
Bodies is an excellent show, but I can see how it might not be for everyone (it has a pretty negative view of British medicine and, in particular, the Ob/Gyn wing, which is only made more interesting by the fact it's based on a book written by a former British doctor).
Spooks is supposed to be good too, but I haven't seen it yet.