Time travel stories, I love a good time travel story. Obviously this would make me a strong candidate to be a Doctor Who fan, although I freely admit to having been in and out over the years. Recently I've been downloading episodes of the current season that have been posted by English fans, and in spite of a couple of shaky concepts they're doing some quite nice stories. (Hopefully this blatant confession won't result in a lightning raid by BBC copyright commandos. Given that I'm in Vancouver, British Columbia, which is damn near the other side of the planet from England, I should be safe unless they have some kind of agreement with the CBC black ops teams. But I digress...)People assume that time is a strict progression of cause to effect, but actually, from a non-linear, non-subjective viewpoint, it's more like a big ball of wibbly-wobbly, timey-wimey stuff.The Doctor, Blink
The most recent Doctor Who episode is entitled Blink, and deals with the sort of time travel opportunities that are parodied in Bill and Ted's Bogus Journey - decide to use your time machine to go into the past to set up things so that you win a fight in the present, then go back to set things up after you win the fight. In this case the Doctor gets sent back in time without the TARDIS, but sends messages to someone in our time to get it back - and then gets the information he needs to set things up after everything is resolved, but before it takes place in his personal timeline.
This directly addresses the real question of time travel: can you change the course of events? The two basic philosophies here are that you can't change things in the past because you didn't - commonly known as the Grandfather Paradox - or that it's an open field, in which future events exist in an indeterminate state. (For those unfamiliar with the concept, the Grandfather Paradox is as follows: build a time machine, go back to the past, kill your grandfather at the age of ten. As a result, your father is never born, you're never born, and you don't build a time machine. So you DON'T go into the past, you DON'T kill your grandfather, your father IS born, you're born, you build a time machine... It's easier to assume that the gun must have jammed when you tried to shoot the little bugger, or, in the big picture viewpoint, if you went back in time to kill Hitler before he starts the Nazi party, you'd fail, because history records that he did start it.)
Both of these philosophies have given rise to some interesting stories, although the approaches required are wildly different. The landmark story for the open field approach is Ray Bradbury's A Sound of Thunder. All you need to do is to step on a butterfly while trying to shoot a dinosaur that's going to die anyway, and the result is a slightly but significantly changed future. (This begs a bigger question, which is why anyone with a time machine would waste their, ah, time running tours into the past so that people can shoot T. Rex. If things were at the point where it was that popularized, I would think that flattened butterflies would be the least of your worries.)
The cast-in-stone position is less obviously interesting, simply because it's less exciting. Going back in time with an anthill and coming back to find out that the ants have evolved into the dominant species and destroyed humanity is a bit more of a climactic ending than coming back and finding out that they haven't. The predestination stories tend to read a bit like inverted detective stories, with the characters running around like mad making sure that all the clues are in place to ensure that the crime happens. There's often a loose thread that miraculously weaves back in at the end, just to ensure that all's well historically. A good example of this would be Connie Willis' To Say Nothing of the Dog, which is rather like the time travel version of The Importance of Being Earnest.