Many years ago I played a Doctor Who RPG via email with several other fans like myself, as I couldn't find any players in my area. The game rules we used were
TIME LORD: Adventures through Time & Space by Ian Marsh and Peter Darvill-Evans, published by Virgin in 1991. What fun it was taking the role of a character in the same universe of my favourite TV series & having adventures! For those who don't know, a role playing game is a game which requires a few dice, rulebooks & lots of imagination -
Dungeons & Dragons &
Gamma World being some of the first examples to hit the market. I could explain more, but i'm lazy - so
here's a link if you wanna find out more.
There have so far been two RPGs based on DW to hit the market, the first was FASA's
Doctor Who Role Playing Game in 1985, and followed by Virgin's
TIME LORD in 1991.

I personally prefer the
TIME LORD rules because, in my humble opinion, they fit the feel of the show better than FASA's version. The only downside is that
TIME LORD was not marketed very well & produced no supplements (other than a DWM article) like FASA's version did.
Still, the future of role playing in the DW universe is about to change, with the announcement for
Cubicle 7 Entertainment to release the
Doctor Who - Adventures in Time and Space Role-Playing Game early next year. Not much info yet, except that those who have play tested it give their thumbs up.
Well, in the mean time you can download
Time Lord online
here as it has been released as a
free PDF by it's authors.
So, get your mates together for game & have loads of fun! Oh, and you might wanna throw
Abslom Daak in there somewhere too.