First, let me say this: Doctor Who is my absolute FAVORITE TV show of all time. Hands-down. The plot is ingenious, the acting is wonderful as always, and the writers behind the scenes are true sci-fi geniuses.
Now. Onto the actual review.
Doctor Who varies in appropriate content for the young 'uns. The earlier 'classic series' episodes are clean, slightly cheesy fun for the whole family. The newer ones, however (I'm talking the Matt Smith years - the episodes airing on BBCAmerica right now) have some 'questionable' content. Mainly, innuendo. In one of the episodes, Amy does her best to seduce the Doctor (but fails) and River Song's appearance is usually accompanied by some mild innuendo as well. On the violence side, most of the episodes are fine for kids 11 and under, with only a few exceptions: The Empty Child (from the Eccleston years, aka 'season 1...it frightened many a member of my family), and of course, Blink (from season 3), the latter of which was so scary that even I, a 13 year old at the time, had to sleep with the covers over my head for a few nights. But, as CrazySense so accurately put, on some occasions the scariest 'monster' is the Doctor himself - the final days of Tennant (the 10th doctor) showed us his darker side in the Waters Of Mars (one of the best episodes done by him, as well as both parts of EOT - 10's last words and his desperation to stay alive as well as his expression when he finds that that is no longer possible continue to jerk tears from my eyes, even after I've seen it numerous times) and even Matt Smith has his moments when we begin to wonder what exactly is going on in his head at times. But, to summarize things, DW is a cultural icon in Britain and I can understand why: it is one of the most ingenious and innovative show that I've ever seen and I would recommend it for kids 12 and up!
Allon-sy! Bowties are cool!