There is a Torchwood episode.. Series 1 Episode 2 - First Day, where a girl gets possessed by an alien.

There is an episode of Doctor Who, unrelated to Torchwood, I don't know the series, but I believe the episode is called "Fear Her" where a young girl is possessed by a very small alien who normally lived in colonies and crashed to earth in a little space ship, and got paved into a pot hole who is drawing pictures and abucting people... I want to say it was Rose who was the Doctor's companion, and it was David Tennant as the Doctor - so maybe Series 2 - not sure....

Those are the only "possessions" I can think of off the top of my head...

I would checkout BiggerToons, they have like 125 DVD videos on Doctor Who which includes all of them including new and old.