I tend to subscribe to the idea that time travel alter history and would lead to the creation of a new, divergent universe,
and so you cannot travel to your own past.
The moment you set foot in the past you create a new future which is different from the one you left.
My time travel rant is here;http://www.orionsarm.com/intro/WhyNoTimeTravel.html
I agree with this view point, which is compatible with the Everett interpretation of Quantum Mechanics.
There are many things we could say about time travel. According to Stephen Hawking, a time machine isn't able to travel before its own construction. So you wont be able to visit Newton to kill him. However, if a time machine was build before your own birth, you could travel to a moment in time before your own creation and kill your mother. Then a paradox.
In classical general relativity, there are many solutions which describes space-time with closed time-like curves (Kerr-Newman solution, Godel universe, and worm holes are well known examples), which means you could use them to travel in the past.
But there is a Fondamental principle in physics : consistency of Nature. There is no paradoxes in Nature, whatever you're doing. Coherence of a theory is the most important thing. Because of this, relativity theory implies THERE IS NO FREE-WILL IN ANY CLASSICAL SPACE-TIME ! So you can't decide to travel in your own past to kill your mother. Even if a time machine was possible, you can't use it as you wish, because you don't really have a free will. Let me explain this.
In classical relativity, space-time is the set of all events, in space AND in time. All events are actually lying there, "somewhere", and they all "coexist" already. Everything is already "writen" in space-time. Relativity theory, when placed in a fully classical context, is deterministic and FATALIST. You can't change any event, because all events are already "memorised" in space-time. There's no place at all for free-will. So even if time travel is possible, you can't change anything. There is no paradox at all. Only coherence of space-time count here.
But if you really believe in free will, and aparently we have access to free will in our real universe, then the space-time of relativity theory must be demultiplied in some infinite set of space-times with many variations (the Multiverse). All those space-times are deterministic and fully fatalist, but you don't know in which space-time you are living. They becomes probabilistic. Your future isn't really "writen" somewhere, because now we have an infinite set of space-times.
Actually, space-time in classical relativity theory is just a usefull concept, a tool, to describe reality. But space-time isn't "real". It's just a representation, a partial map of events. The real space-time doesn't even exist (in the sense of relativity theory). There is no future "coexisting" with the past, and the past itself is disapearing at all moments.