Hi,
Time travel brings a whole swathe of paradoxes with it. First there's the grandfather paradox - go back in time, kill or make it impossible for your grandfather to have kids, and poof you're in trouble. Clearly if he couldn't have kids you were never born, but at the same time if you were never born you couldn't go back in time to annoy your grandfather. So you become in essence, Schrodinger's cat.
Next as others have mentioned there's the time tourist problem. Everybody from when time travel is invented wants to go back in time to see certain events, the crucifixion for example. Now that's everybody from the infinity of time that passes by after time travel is invented. So just how many time travelling people would be in the crowd? Thousands, millions, billions, trillions?
Of course there's the issue the time travel destroys free will. Say you go back in time to watch the crucifxion. You make no changes except for one tiny one, you were there. Now if we assume that that is fixed, then everything else that occurred after that point until the point where you went back in time, must also be fixed. The slightest change anywhere along the time line between the two points could result in you not being at a point where you could not go back in time.
Of course it also violates the conservation of mass / matter / energy laws. (Maybe they're just guidelines eh?) But lets face it if everyone who time travels weighs say eighty kilo's then the universe in the past is suddenly eighty kilo's larger then it was an instant before the time traveller arrived, and the universe in the future that he left is eighty kilo's lighter. In effect matter has been both created and destroyed. Now that may not sound like a lot, but what say a million people suddenly pop into existence at the crucifixion? Now its eight hundred thousand kilos. What say its a billion, or a trillion people? At some point the mass increase and decrease will be so large that the orbit of Earth will be changed. That could stuff things up.
Cheers.