I once asked the writer Douglas Adams ("Hitchhiker's Guide to the Galaxy") if he had anything to do with these series, and his response was, "No, but they're all friends of mine." That explains a lot right there.
I first saw this series on PBS, and it absolutely floored me. The humor is razor sharp, the dialog fast and funny. The first series is a little weaker in this regard, but very, very funny in a way different than the later series. The fourth, in my opinion, is the weakest of the bunch, too ofter falling back on gross out jokes, but even that is better than a lot of other stuff coming out of the BBC. The Christmas Special is outstanding.
Keep an eye out for an appearance by Tom "Dr. Who" Baker as an insane legless ship captain in the second series. It was a testament to his performance that I, a big fan of his best known role, did not recognize him after having watched the episode about five times... until someone pointed him out to me. The Blackadder series are graced with a great supporting cast, including Brian Blessed, Miranda Richardson, and a number of other actors of whom you may never have heard, but should get to know.
If you are turned off by cynical humor, this show is not for you; but for anyone else, it is absolutely worth checking out.