I'm okay with being pictured as the great David Tennant. He's much funnier than I am, for starters.Today is the 50th anniversary of Doctor Who, so there was a big 50th anniversary episode (it'll be reairing on BBC America for the next several days, it's called "The Day of the Doctor") with *all* the Doctors in it and a plotline chock full of 50 years of the show's history. It was really well done and possibly a good starting point for interested parties.
If you want a more straightforward episode to start with, check out "The Next Doctor" - it's a steampunk-y Christmas episode with just David Tennant, but you don't need any previous Who knowledge to understand what's going on. That's the one I usually show to people who have never seen Doctor Who.
An Adventure in Space and Time was a docudrama the BBC did in celebration of the 50th anniversary, and it tells the story of how Doctor Who got greenlighted in the first place. (The short answer is "with great difficulty" because the BBC didn't want to make a sci fi show, and "only thanks to the first female producer in television, who really believed in the idea of a sci-fi show that the whole family could watch.") They really got all the details right, from casting to lighting... it feels like you're just a fly on the wall, watching them struggle to make a show that almost no one believed in and that was something completely new.
Without Doctor Who, there probably wouldn't have been Star Trek, or anything that came after it. Doctor Who was the show that proved sci-fi could work on tv... and it's still around, still telling the story of a mad man with a flying blue box, who'll (usually) use only his brain to win a fight with the baddies, who can change his face, and who can travel anywhere in space or time.
Somethin' like "the bigger the toys....." 
Here is a link if you want to watch it 
