So I guess Richard Curtis' film About Time is due to come out soon (time-travel romcom), so the Guardian put together a list of "top 10 time-travelers" that led to the following YouTube link for an entire series, Goodnight, Sweetheart, about a man who pops back and forth between his present and the WW2 era, to...cheat on his wife in the past, I guess?:
http://www.youtube.com/watch?v=st72Xd0xRaU&list=PLC512D9B5E2B1E2A2 And a related piece (spoilers for About Time, though mild ones - nothing you wouldn't know if you'd already seen the trailer):
http://www.theguardian.com/film/2013/jul/31/why-cant-women-time-travel (what's interesting about this is that while it might be largely true of film, it doesn't really hold true for TV, and it's definitely not true for books, especially children's/YA ones.)
The piece briefly mentions an anime film that I really liked and ought to watch again, The Girl Who Leapt Through Time - with, I think, the unfair remark that the heroine "doesn't have a choice" and so it doesn't really count. Lots of time-travelers travel inadvertently, including some of the male travelers she mentions (Henry from The Time Traveler's Wife, for example). I think you can go two ways: determined, purposeful time travel (usually via machine), or scary, inexplicable natural or magical phenomenon (time-slip) - and you're doing different things depending on the method you choose. The first is often about exploration, experimentation, or prevention: what happens to time if you do this? what was history really like? can you kill Hitler, or stop the rise of the robots?
The second is often more philosophical and self-oriented: what is time, exactly? what happens to me if I stay here? what makes me who I am? how can I relate to other people meaningfully if I'm hurtling through time, or if they're dead long before I was ever born? where do I belong? Obviously there's overlap - especially if your time machine breaks down or your ride can't pick you up - but I see at least the beginnings of a dividing line.
Which is - and I was doing surprisingly well at not making this about Doctor Who - one of the things I really like about the Weeping Angels, because in a narrative where time travel is often quite controllable*, the Weeping Angels cause anarchic time travel; they force the victims to deal with that second batch of questions, as they're ripped out of their own lives and deposited into the past. (This is also why I love the two-parter "Human Nature/Family of Blood," especially that scene with Martha outside the pub in 1913, gazing up at the stars and clinging to the hope that she'll be back out among them with everything she's got: what happens to her if she has to stay there? If her self-identity as a doctor gets completely dismissed because she's Black and a woman? The historicals are often my favorites, because of the clash of present and past - "Vincent and the Doctor" for the win, for always - but I love "Human Nature" particularly because it's about staying in the past for a long period of time, not just touching down for an adventure and then hopping away again.)
*Insert joke about the Doctor's terrible driving skills here. Or, if you prefer, the exchange from "The Doctor's Wife": "You didn't always take me where I wanted to go!" "But I always took you where you needed to go." But as long as he has the TARDIS, no matter where the Doctor winds up, he's not really in any danger of not being able to get away and go someplace else.