Doctor Who, on BBC One (UK)
Incredibly long-running, classic sci-fi television series from Britain, one of the greatest TV series of all times. There were seven different Doctors in the course of the (original) series, which ran for 26 seasons, from 1963-1989. Well... I suppose first I should say that we don't know the Doctor's name, he's just called the Doctor. I'd rather not know his real name, anyway. Um, the Doctor is a Time Lord, from planet Gallifrey. His race developed time travel long ago. They regenerate, too. They'll live a full life, then regenerate. They're only supposed to be able to do this like 12 times. But they can live thousands of years because of this (they can live hundreds of years within a single generation). Anyway, this gives different actors a chance to play essentially the same role. Except that it's not just appearance that changes when Time Lords regenerate, their whole personalities can change, everything from sense of humor to fashion sense, and so on.... But some things that will never truly change about the Doctor are his sense of adventure, his desire to help people, and his generally maverick nature which sets him apart from the other Time Lords, and keeps him away from his homeworld the vast majority of the time.
First Doctor (William Hartnell), seasons 1-4 (1963-66)
Second Doctor (Patrick Troughton), seasons 4-6 (1966-69)
Third Doctor (Jon Pertwee), seasons 7-11 (1970-74)
Fourth Doctor (Tom Baker), seasons 12-18 (1974-81)
Fifth Doctor (Peter Davison), seasons 19-21 (1982-84)
Sixth Doctor (Colin Baker), seasons 21-23 (1984-86)
Seventh Doctor (Sylvester McCoy), seasons 24-26 (1987-89)
I'd like to be able to talk about each season, but some I never saw and the rest I don't remember well enough. I will say my favorite Doctor was the Fourth, and my second favorite was the Seventh. Anyway, the Doctor has a TARDIS, which stands for "time and relative dimension in space." On the outside it looks like a British police box (similar to a phone booth). The Doctor's tardis's chameleon circuit is busted, which is why it can't change appearance as most tardises can. Anyway, inside it's really huge, because of a dimensional stabilizer that lets the inside be bigger than the outside. Usually we just see the control room, which is right inside the door. But there are lots of other rooms, many of which are very large. You could get quite lost in there. Anyway, a tardis is a vehicle which lets one travel through time and space. The Doctor goes to lots of different times and places both on Earth and throughout the universe. He gets involved in all sorts of trouble and manages to save the day, whatever's going on. There are lots of recurring enemies such as the Master, who is an evil renegade Time Lord; a robotic race called Cybermen, a robotic race called Daleks, and um... plenty of others. The Doctor almost always has companions with him. He's had lots of companions over the years, way too many to mention here, but some of my favorites included Ace, Leela, K-9, and Adric. Anyway, the props and special effects and things could be rather cheesy. But still, I love the show, and it deserves a better description than I can give. So I guess it's a good thing I've provided plenty of links to other sites, which do a far better job than I ever could (particularly some of the ones on my "Doctor Who links" page).
Actually, there's also an eighth Doctor, but he was just in one TV movie in 1996, which could have spawned a new series, but didn't.
There have been plenty of specials and things over the years (some probably canonical and some surely not). And I certainly haven't seen nearly all of them. There was a special between seasons 20 and 21, called The Five Doctors. And there was a spin-off series, K-9 and Company, which only had one episode produced. And there was a spoof called The Curse of the Fatal Death. And in 2013, there was a TV movie called An Adventure in Space and Time, a docudrama about William Hartnell's time as the First Doctor.
Doctor Who was once again revived in 2005, with the Ninth Doctor. Instead of starting with season 27, it starts with series one, but it's still the same continuity as the old show. I've got a separate page for it (later divided into several pages, for each new Doctor). There's also a show spun off of that, called Torchwood.