There is one form of "time travel" that every physicist I've ever met has agreed is possible assuming the premised technologies ever become somehow available. It's silly, but it would work. Oh, and it's also cheating.
What do you have to do? Travel 299,792,458 m/s to the other side of a black hole without going around. Yes, that means basically travelling "through" a black hole at the speed of light. However, the light that is coming at a black hole but is barely "missing" is being bent around the outside edge of the hole, so if you are able to travel from one side of the hole to the other without having to take the long way around that the light is doing, then you will arrive at the other side before your light does. Relative to your beginning point, you just traveled back in time. It's entirely pointless, of course, because you can't influence anything that would happen before you left on your trip, but it is still technically time travel and it wouldn't break any of Einstein's laws to do it.
Aside from this, no. I don't think time travel is actually possible. I leave open the possibility that I could be proven wrong, as any self-respecting man of science would, but given our understanding of the universe, there is just flatly no way to go backwards in time and I don't believe that there ever will be.