This seems like a sensible place to start...
You've picked up the Doctor Who RPG and have a chance at gathering a few interested players. What do you do with it? There are some suggestions in the box, of course, but it doesn't hurt to have a few spare ones.
The Doctor And Companions
It's sustained the show for thirty-one series on and off (not to mention as many years' comics, shedloads of books, audio plays...) so let's start here.
The Doctor, a mad man in a box, picks people (for various values of "people") up and they go on adventures in time and space, battling threats to time and general villainy. "Planets to save, civilisations to rescue, creatures to defeat and an awful lot of running to do." This gives you the entire setting to play with, of course, and you shouldn't have much trouble coming up with adventure ideas.
There are problems, of course. The Doctor is madly powerful compared to the average Companion, of course, so you need a player who wouldn't abuse that. And do you use a canonical Doctor and Companions or not? They vary in style, ability and even power level - and of course, as the new producer, there's always the temptation to have a new Doctor...
Someone Else And Companions
Another Time Lord or equally strange and powerful being. This means you can play fast and loose with canon (like this has ever troubled the series) and skip the need to keep the Doctor consistent so your new Time Lord could, say, settle down and raise a family. The trick here is to make the new "title character" different enough that it couldn't just as easily be another incarnation of the Doctor.
Lost In Time
Of course, while you might need a Time Lord to control a TARDIS, there are other forms of time travel out there as well as the uncontrollable TARDIS option, and a group of ordinary-ish sentient beings could end up inside one, bouncing around time randomly and getting in trouble without a handy guide. Good for the feel of the early black-and-white series where the Doctor wasn't so ruddy amazing and it was his first time meeting Daleks, Cybermen, and so on.
A group of Time Lords, Time Agents, or other heroic-type problem-solvers going through time with a defined purpose, being sent on missions rather than fated to stumble into adventures. Nice and straightforward, so that's about all I need to say on the matter, so I'll just add that GURPS Time Travel is pretty good on the subject, particularly the example setting where two rival time agencies are both trying to alter time to make their future the real one.
The Sarah Jane Adventures
The Whoniverse is wild and woolly enough that you can save the world from your attic in Ealing. You'd be skipping the time travel rules and the like (apart from the odd time warp episode here and there) but consider the kind of things a group of normal-ish Earthlings could easily get mixed up in. Imagine a Sparrow And Nightingale series, fighting alien threats with book learning, a laptop computer and maybe a set of night vision goggles if they go and buy them.
As above but with guns and swears. The Doctor Who game isn't a good fit for it - drop the initiative system for starters. And would many players be keen on being quite as useless as that shower? It's a prominent has-its-own-show example of an idea that fits in the Whoniverse but not in the spirit of the main show or the game as written. I wouldn't want to play Abslom Daak, Dalek Killer under this ruleset either.
As above but without swears. More capable than Torchwood, although still prone to grumbling about bullet-proof monsters. Also brings in chains of command and things like that, although it always has civilian specialists and room for Companion-style hangers-on with no official rank or jurisdiction.
What else could you do with this game? Well, it's pretty geared towards reflecting Doctor Who, starting at talking-beats-fighting built into initiative. There aren't many settings that are anywhere close to as let's-talk-about-this. It would be a great initiative system for some specific characters, but few of them define their settings. Still, it could work for a group of disparate characters prone to talking and running in a Who-like style.
By way of example: The Flying Dutchman. People who have taken a wrong turn, literally, and are now adrift in the Seas of Time, pitching up seemingly at random in different times and places where Time has gone astray. A bit like Sapphire And Steel but without the PCs themselves being mysterious and otherworldly.