For Spooks I’d recommend staying within the safe boundaries of series 1-3. Beyond that it’s a downward spiral into crapness.
My own recommendation would be series 1-3 (again, before it got crap) of Shameless and series one of Skins which are channel 4 productions. Not sure if they’re available internationally but they’re blummin brilliant! Oh, and the UK version of the Apprentice which I’ve only just got into but it’s FANTASTIC!
Look out for ‘Black Books’ too. It seems to have fallen under the radar, it’s one of my favourites alongside Red Dwarf.
I remember that now, it was quite good.
All my favourites have been mentioned but one, so I’ll throw in “The League of Gentlemen”.
I disagree that Shameless got crap. It changed, it grew, and of course there were weak moments along the way, but it’s come a long way from its original (brilliant) cast into a much larger organism. It’s always kept its sharp dialogue, unpredictible plot lines, and fantastic one-liners from Frank and others.
Edit: Skins is crap, though, despite its good scripts and some bits of good casting. So there. 
Look Around You is a great send up of educational TV. I don’t know if you can get it on DVD here, though.
And there’s a show that’s all about television that I watched entirely on YouTube. What is that called- I forget. It has the Grandaddy song in the intro… Ah, yes, Screenwipes. It’s a lot of ranting and fun.
I was a big Dave Allen fan, and would love to see his shows again. Another show from the mid-70s that I liked was No, Honestly, which reminded me of the old Burns and Allen shows.
Robin Hood is good, in my opinion. An interesting take on the legend, and I’m considering picking up the first season which is out on DVD. The second season started airing yesterday on BBCAmerica, and it looks like theyve got some interesting things planned.
Big Train is the funniest sketch comedy show I have ever seen.
Spaced is fantastic (and will be released in the US this summer, according to Edgar Wright)
Jekyll–Written by Stephen Moffat of Coupling and Blink fame. Awesome, awesome show. Only 6 episodes and available in America on DVD.
Life on Mars
Father Ted Not as funny as the other comedies to me, but the whole series is worth it for one more glorious moment that made me laugh so hard I almost choked: "PLAY THE FUCKING NOTE! NO! NOT THAT NOTE! THE OTHER FUCKING NOTE!
The first series of Shameless is available on Region 1 DVDs (but not the subsequent series) and Sundance Channel is broadcasting the second series
(although today they’re showing the ninth episode, so they’re pretty far along and I don’t know if they’re going to start the series over). It’s one of my favorites as well. And second the recommendations of Father Ted, Coupling and Black Books. All are hilarious.
If you don’t have a Netflix subscription, you might want to get one, as they have many British series available.
Do you mean Charlie Brooker’s Screenwipe? If so, I’d say that that’s very limited in it’s appeal as it deals with mainly British TV and media. If you liked that you should check out Charlie Brooker’s Guardian columns. Charlie Brooker’s Screenwipe is essentially his TV-based column (Screenburn) filmed for the BBC with a lttle extra material.
I really like Robin Hood but if it’s historical accuracy (or even relevency) you are looking for- you won’t find it here. Often, his gang sports modern clothes- camo, sneakers, watches- it’s kinda fun spotting it. I noticed “Jaq” has a cute new hairdo this season. It’s really tongue in cheek and campy- you’ll hear things like “I shot the sheriff, but didn’t shoot the deputy” and other goofy stuff that, if you don’t take it too seriously, really makes the series IMHO. Aside from very few “deaths” (Robin is against killing anyone, apparently, and the sheriff and his man are very good at putting Robin into easily escapable situations when they had ample time to get rid of him) and not much suspense, it is at least action packed and quick moving. Robin, Marian and Guy of Gisborne are all great characters at least with some depth to them. And the sherriff is cheerfully evil and funny.
Ditto to the above reccomendations on** Extras ** and I also love **Kitchen Nightmares ** and MI-5.
Most of the shows I’d reccommend have been listed, so I’ll add one that hasn’t been mentioned yet: Absolutely Fabulous. Two ladies who are best friends, and they spend their days drinking and wearing outlandish clothes and drinking and swearing and drinking and giving the one lady’s daughter hell (she’s the only “normal” one) and drinking…
I haven’t met too many people who’ve liked it, but the ones who do swear by it. (Myself included.)
Looks like most or all of mine have been listed, but I’ll repeat for emphasis! 
**Black Books
MI-5 / Spooks
Blackadder
Coupling
AbFab
Red Dwarf
Yes. Minister**
Which reminds me: near the end of last night’s episode, when Robin was being rescued, I swear I heard two of his men say, “So it’s goodnight from me.” “And it’s good night from him.” Which were the closing lines of every episode of *The Two Ronnies", previously mentioned by Quartz.
Ah, if I only had time to make a definitive list…
I haven’t seen any suggestions here that I violently disagree with (I disliked A League of Gentlemen, but it started off OK). I’ve been a huge fan of British TV and, lately, radio for a long long time now. Mostly radio these days due to lack of TV watching time. I’ll add in Have I Got News For You and Mock the Week, though you need to be up on British news to get most of the jokes.
I’ll look into that, thanks!
I don’t know about limited appeal; I live in Minnesota and haven’t been exposed to a lot of the particular media he covers but I was able to appreciate the ranting about media in general. Plus he has a particular ranting style that I like a lot, like the guy who does Zero Punctuation (video game reviews). And he does do a whole episode about American TV and often mentions American shows. But it could just be my taste, and upon further reflection you might be on to something by calling it limited appeal.
Note to those who love british tv shows: try your public library for DVDs. Chances are if they don’t have them, they will be able to interlibrary loan them for you.
Yes, I’m serious.
Yes - that was pretty good - they repeated it on one of the freeview channels recently and it’s still good. I’m a big, biased fan of Fry & Laurie anyway, but it’s my distinct impression that Jeeves and Wooster can’t ever be done any better than this.
Huh. I didn’t enter this thread earlier because I figured all the best shows would be mentioned already. Not so much.
Foyle’s War is brilliant, flawless, some of the best television ever, from either side of the Atlantic. I recommend it unreservedly, to anyone, with any kind of taste. It’s that rarest of things, art which is both excellent and widely appealing. But then, don’t let me oversell it. . . .
Just as good–some would say better, and I’d have a hard time arguing with them–and also not yet mentioned–is the Helen Mirren series, Prime Suspect. Easily among the 2 or 3 best cop shows ever mad. Brilliant. A bit darker than Foyle’s War, so probably with more limited appeal, but brilliant nonetheless.
And nearly equal to these, the even darker–but, yes, brilliant–Cracker, with Robbie Coltrane as a deeply (but deeply) flawed man who works as a consultant for the police; he’s a psychologist with (here comes the cliche) a particular talent for understanding the criminal mind.
These three shows are on my shortlist, if I ever have to go to a desert island with a dvd player.
Sadly, as seen here, most of the classic shows listed here are 10 years and up to 40 years old… British drama and comedy has been a bit lacking of late, and the highlights on telly is the quality US dramas (though the comedies are lacking a bit though in quantity).
Some recommends not mentioned before:
Absolutely - Just coming out on dvd in the uk. Surreal and excellent.
Monkey Dust - Last good BBC3 comedy.
I think most of the rest have been mentioned. Spaced is particularly good. Father Ted too.