I used to watch Dr. Who many years ago (the Fourth Doctor was my first time seeing the show), when it started airing on PBS in the 70's. Then it sort of faded away here in the states, but my friends in the UK have watched for ages. I was reintroduced when the new episodes began on PBS a few years ago with the Ninth Doctor (Chris Eccleston) and only watched because I loved him in Heroes. That got me hooked again, and I watched all of those and the series with the Tenth Doctor (David Tennant). I've seen one of two with the new doctor (not fond of him, he's too young and makes me feel old..
). I've also just started watching Torchwood (which spun off of Dr. Who during David Tennant's series). Torchwood is an anagram of Doctor Who. I actually like it better than Dr. Who, but that's just me.
If you can find it, start with "Rose", it's the episode that introduces Chris Eccleston as the new Doctor, and he explains who he is and the whole time lord thing.