Yes and no.
All time travel depends on how restrictive time travel is. There are several types of time travel!
Note that if everybody had a time machine, Hawkins should have had a booming party on 28th of June 2009, to which he sent out the invitations on the 29th of June. He gave it to remind of his 1992 conjecture that travel into the past is effectively impossible.
Whenever you travel back and try to prevent something, you create a closed 2-state loop for yourself, and are therefor forever trapped in either of the states.
- Jack Traveller travels back 50 years and prevents his grandfather Albert Traveller meeting his grandmother Janine Jacobs by running him over with a car. Because his gramps never met Janine, Peter Traveller and his son Jack Traveller are never born. Because of this, Jack - who never existed and ceased to exist the moment he ran over Albert - never traveled back to even start the car to run over his grandfather Albert. Because Albert wasn't run over, Peter and then Jack get born. Jack travels back 50 years and runs over Albert...
Grandfather Paradox at its finest - Gramps Albert, Peter and Jack have become Schrödinger's Cat, the existence of the later 2 dependent on the state of the first, which is simultaneously dead and alive until we manage to collapse the quantum formula!
Closed timeline loops
Quantum mechanics tells us, we only need to look for Jack after the point of time-travel and we can collapse the whole thing: If Jack exists there, he never traveled and Gramps never died. If he doesn't, then Jack had never existed in the first place.
Don't change the past!
But you can certainly can do 12-Monkey style time travel with this: DON'T CHANGE THE EVENTS, but send notes to the future, where they will be received after the point of departure! This way causality is saved, Grandfather paradox avoided.
You can't change the past. Or as Dr. Who said in The Aztecs: "You can't rewrite history! Not one line!" It's a little up to interpretation how this can be seen, but the gist is:
If you attempt to change the timeline there's only two options: Your very attempt to change the timeline is either doomed to fail or by some thing or another your very action only did create the timeline you traveled from to begin with.
- Jack never knew his grandfather who was killed in a military accident. When he travels back 50 years to try to meet him, he runs over his gramps before he meets his grandmother. Later he meets a girl - Janine Jacobs - in a bar and (after kicking Private Paul Pascal's ass) things lead to one another and they dance the horizontal tango. 9 months later, Peter Traveller, Jack's dad is born and some 25 years later, Jack.
Jack had to make the timeline happen the way he had known it after he traveled back. And if he wouldn't have been the one to dance with his Grannie, it would have been Private Paul Pascal, who fathered Peter. In either case, Peter was never (even before the time travel happened) the son of the Albert Traveller to begin with like everybody thought!
A variant of the general timetravel rule is explored by The Butterfly Effect. It imposes one extra limit: One can only travel backwards and only to his own past, taking control of his own body back in the event one travels to, and displacing the previous consciousness.
For an inside observer, the timeline fluctuates, but no other but the time-traveler does even know that anything changed. Only one state of the possibilities created by the time-travels exists: the one that was created by all the changes culminated. And since only the time-traveler can remember those 'alternate pasts' created by his time-travel, his mental health suffers.
There's no time-travel, it's travel to a replicate of the world.
Instead of really traveling back to your past, you travel to an exact copy of the universe as it had been before your interference. By your interference that universe develops differently - but you don't really have effected your native timeline. Depending on the rules, he can travel back to his native timeline (and see nothing changed) or he travels to the point later in the new timeline. Or, by traveling back, you actually kill yourself.
- Jack Traveller travels back 50 years and (once again) runs over his gramps before he met his (former-future) grandmother Janine. In this new timeline, Janine becomes a nun and neither Peter Traveller nor Jack Traveller are born. But there is the Jack Traveller not native to this timeline.
Only in such a setting time-wars are actually somewhat feasible, but they end with all sides winning simultaneously, as each generates its own alternate world that never had enemies to begin with. And each dissident group branches off into its own, perfectly controlled dystopia of different means...