The Different Time Travel Rules

Back to the Future 2 and Star Trek Rules:

Going back in time creates an alternate timeline that you follow when you go back to the future. Both timelines exist and it is impossible to just jump between them without changing events.
As Ben "Yahtzee" Croshaw put it "you can change shit but the timeline seems all pretty cool about it". An alternate reality.

Back to the Future 1 and 3 rules

There is one timeline and the things you do in the past can affect everything else about you it seems except for your memory. It is possible to erase yourself; and that results in you losing your ability to play the guitar while you fade out.

Futurama and Harry Potter 3 rules

You can go back in time and do whatever the hell you want, because as it turns out you were supposed to do it in the first place. And in the case of Harry Potter, the universe will subtlety frame your eyes (the camera) so that the non-time-traveling people don't notice. "Don't do anything that would interfere with the timeline, unless it turns out you were supposed to do it, which, for the love of god! Don't not do it!"

Lost Rules

Pretty much the opposite of the previous rules. You can go forward or back in time but you can't change any events that are supposed to happen. For example, the premise that you could go back in time and kill yourself and create a paradox would not happen because you would not be able to kill yourself, you would always fail. "Tell me, did the gun jam on you or did the bullet just bounce off of your skull?"

Terminator Rules

Kind of weird: "Maybe you can change shit, but then maybe you can't change shit, and then you go make a god-awful TV series and Christian Bale yells at someone".

The Time Machine rules

You can't go back in time if it would result in a paradox, and you can't go back to before the time machine was created, otherwise you can go forward in time and then go back to when you came from.

The Butterfly effect rules

Going back in time always creates a different future or a paradox, there is no avoiding it.

Hot Tub Time Machine rules

When you go back in time, you inhabit yourselves in that time but you retain your memories of the future. Like as if you get to do-over that part of your life. Except if you didn't exist yet at that time, then the Back to the Future 1 rules apply to you.

This guy's rules

This would theoreitcally be the real world's rules.

Prince of Persia Rules

Only one person can control time at a time. The timeline goes back and forward when he wants it to and he retains memory of traveling though and back through time.