Is time travel possible?

We have been haunted by this question for quite a long time and some of us may have given up by now and reached the conclusion that time travel is something that is only plausible in science-fiction movies and books.
Most of us are familiar with the idea of time travel through movies such as The Time Machine (1960), Déjà Vu (2006) and Star Trek (2009).
But can we actually look at the possibility of traveling through time without breaking the physical laws of our Universe? Will it always be an unanswered question or will we find a way to finally reject or accept a theory of time travel?

Here you can read an interview with theoretical physicist and cosmologist Paul Davies about this matter.
+ watch here the video where theoretical physicist Michio Kaku explores the possibilities of time travel.