Blackadder, on BBC One (UK)
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This program consists of four separate limited series. The first series was called The Black Adder, and it was set in 1485. The second series was called Blackadder II (IMDb), and was set in the latter half of the 16th century. The third series was called Blackadder the Third (IMDb), and it was set in the late 18th/early 19th century. The fourth series was called Blackadder Goes Forth (IMDb), and it was set in 1917, during World War I. There have also been a few specials, though the only one I've seen was Blackadder's Christmas Carol.

For now, what I can tell you is that each series is set in a different period of British history. The main character is played by Rowan Atkinson, and this is his best role (or roles) that I've ever seen him in. In the first series he is a duke named Edmund (but he calls himself "the Black Adder"). In the second series he is Edmund, Lord Blackadder (Wikipedia says he's the great grandson of the original character, something of which I was never aware when watching the show). In the third series he is E. Blackadder, Esq., butler to the prince regent. In the fourth series he is Captain Edmund Blackadder. I suppose the characters are all related. Each one seems to have a lower station in life than the last, but also seems to be smarter than the last. They're all rather sarcastic and quite funny. I think the only other character who really is in all the series is Baldrick, who is always pretty much the lowest class and stupidest character, but always loyal to Edmund, and always quite funny. Other actors may recur between series, playing perhaps similar roles to their characters of the past. Oh, and I should say that each series is only six episodes long. But the show is always bloody brilliant and clever and crazy and inspired and witty and hilarious and jolly good fun and... I guess that's all I can say, for now.