I like a lot of the older British TV shows that get put on Public TV here. Stuff like “ARE YOU BEING SERVED”, “FAWLTY TOWERS”, and “KEEPING UP APPEARENCES” I find to be great comedy. I’ve noticed that my parents like them, probably because the 1970’s British shows are a lot like the 1950’s American Comedy shows.
Anyway, what can we expect toget over here in the years to come? Are you limeys still making KUA-that’s a really great show!
PLEASE don’t send us any more shows about country parsons and their crumbling churches! 
Pretty good, especially with regards to comedy: The League of Gentlemen, Shameless, Little Britain, The Office, Alan Partridge etc.
It’s dark. The Office is pleasantly uplifting, compared to Monkey Dust and Shameless, which are IMO by far the best programmes at the moment. Monkey Dust is an animated comedy, rather surreal, and very sick. Shameless is a comedy-stroke-drama, set on a rough Manchester council estate, and is sometimes quite spooky in its realism. In general, The Office and its ilk have driven one of the final nails into the traditional sit-com studio-audience format. (Keeping Up Appearances stopped being made many years ago.)
As for drama, I can’t think of anything worth mentioning. Certainly nothing to compete with the stuff HBO has been providing over the past few years.
I think it’s fair to say that there haven’t been any decent mainstream British sitcoms for quite a while now, unless The Office counts as mainstream. The best TV comedy produced here in recent years is of the “ironic panel game” genre - Have I Got News For You, Never Mind the Buzzcocks, Shooting Stars, etc. These are essentially excuses for invited stand-up comics and other wags to be funny, in the format of a quiz show. They have been staples of British TV for the last fifteen years.
Traditional British sitcoms are few and far between. There’s quirky or satirical stuff like The League of Gentlemen, Black Books and Phoenix Nights, but not much in the Dad’s Army or Only Fools and Horses vein. It sounds like you have already seen The Vicar of Dibley and been duly unimpressed. Don’t expect to much of My Hero or My Family, either. One Foot in the Grave is worth a look if it isn’t already on PBS.
Except I forgot about the Irish/British Father Ted. If one of the hallmarks of a good sitcom is that it is funny to sophisticated and non-sophisticated viewers alike, then Father Ted is a very good sitcom. Whimsical, absurd, very funny.
There are a couple of Dramas with popularity - Frost, Judge John Deed. They are too slow (and not on at the right time/day) for me, but they seem well made.
I don’t think anyone mentioned the Royle Family.
There’s also Nighty Night, Time Gentlemen Please (not very good IMO), Black Books, Spaced
Going back a bit there’s Men Behaving Badly, Red Dwarf,
But most of my favourite programs are American…
Simspons, Malcolm in the Middle, Oliver Beene, Two and a half Men, Frasier, Friends, ER, Rescue Me (bit right-wing but meh), Las Vegas.
It’s gone downhill since Blackadder finished! Then again, since nothing could ever match Blackadder, it was inevitable ;).