You're not thinking fourth dimensionally!

As some of you may have guessed, I am a huge fan of time travel entertainment. I find the entire concept fascinating, which is interesting because I also think that time travel is completely impossible. And I think that is what captures my imagination - it is impossible to do anything wrong in a time travel story.
Think of it this way: if time travel is impossible, that means that if you are going to do a time travel story then there are no 'rules' to follow except those that you set yourself. That means you can ignore the paradoxes that you want to and enforce the ones that suit your story. Anything becomes possible once you start at a point of complete impossibility.
I often find myself shaking my head at people when they start picking apart the 'logic' of time travel stories and start talking like experts on how it 'should' work. There is no 'should'. Even theoretically there are no rules for time travel. I don't really think there is any sort of scientist who has come up with theories about how time travel would definitely work. Using some of Einstein's theories it has been speculated that time travel may be possible, but only forwards, never backwards in time (which makes a return trip kind of hard).
That means, as soon as you have a time travel story then there are no dictums that must be kept. If you want it to be possible for a person to survive the murder of their own grandfather, then they can. How? I don't know, maybe once a person travels in time he/she is protected by a quantum force that sets him/her outside of the space-time continuum, meaning all other changes do not affect him/her, including the erasure of his own bloodline. Sounds like a paradox, but we've already broke the impossible barrier by having that person travel back in time, so what is wrong with having something else impossible happen? I say, nothing!
With all of those impossibilities thrown out of the window it then allows for any type of story to be told. The best way to tell the story, of course, is to pick a set of rules to follow and follow them, or to completely ignore the issue and tell the story. Really, it's up to the creator.
Best time travel movies in my opinion are: Back to the Future (Parts 1,2, and 3) and Butterfly Effect.
Best time travel stories are written by Phillip K. Dick. I've really only read his short stories, but there are a few that deal with time travel and they are very interesting. I highly reccomend reading his work.
Best time travel quote: "One hundred years ago? That's this year!" Doc Brown in Back to the Future III.