I'm a little late to the game, but I just finished reading Michio Kaku's great book, Parallel Worlds, which discusses the Physics of many strange things, including Time Travel. Einstein was apparently the one to open the door to time travel by allowing for the possibility that traveling in wormholes  through folds in space and time would allow us to  hypothetically escape to not only another  place but another time as well.

For those of you itching to get into the garage to start making you own Time Machine, I wouldn't start gathering components just yet, however. The scientists who are dedicated studying time travel are finding out that there are more problems than solutions with actual Time Travel, mostly revolving around the wormholes themselves.  In order to stabilize the wormholes, negative energy is needed to counteract the light energy given by the light rays at the entrance of a worm hole to keep the wormhole from collapsing. The other problem is finding the wormholes, which are located in space-foam. Physicists including Stephen Hawking have conducted numerous mathematical and thought experiments to determine if time travel is really possible.  Sadly, Steven Hawking himself believes that time travel is high improbable at best after he conducted some thought experiments.

Despite this, many physicists are still interested in the paradoxes of time travel itself. According to Kaku, there are four types of paradoxes which I will attempt to paraphrase here:

1.  Grandfather Paradox. If you kill your Grandfather, (or do something to prevent him from being born), you cannot be born.  This also refers to any action you might make in the past that would prevent your own birth.

2.  Information Paradox. This is a little tricky, but goes something along the lines of this, if your future self gives you specific information or technology from the future, it doesn't really exist because it has no origin. (sounds a little flimsy to me, but then again I didn't even take high school Physics so have nothing to say about this.)

3. Bilker's Paradox.  Let's say you know that you are going to work at Microsoft in the future. If you choose instead to work for Apple, you are then making your own future impossible. 

4. The Sexual Paradox. This is the ickiest one in my opinion. In this case, you become your own Dad, which is almost what happened to Marty in Back to the Future when he traveled back in time to meet his mother.