There are many theories on the possibility of time travel, ranging from clueless guesses to careful, informed decisions. This, along with many years of science fiction writing and movies, has clouded the debate somewhat.
I am fascinated by science, from Newtonian physics up to the latest advances in speculative quantam theory. However, I am no expert although I do have an abundance of common sense and this is where I would like to base my argument from.
Time travel into the future is of course possible as we are all travelling forward through time. As has been proven through experiment, time can even be slowed down in respect to a person travelling at high speeds. So it's possible for a person to travel into a future that would ordinarily be beyond their life span. I feel though, the main point of the question is if it is possible to travel in the opposite direction and go back in time. Common sense tells me this is not possible and never will be, at least not to humans.
If our species does perfect time travel at any point in the future then we will ba able to visit any time up to and including the time we currently occupy. Now, I'm sure there will be safeguards in place to stop things such as the assassination of Hitler or preventing the 9/11 attacks. However, knowing humans as we do, is it at all feasible that there wouldn't be at least one person who would either obtain or develop time travel, if it is possible, at some point in the future and do something that effects our time now? No matter what safeguards are in place for modern technology there are always those who will try to exploit it for their own gain, fame or notoriety, so why not in the future?
If time travel is a possibility to us at any point in our future, then there would be some evidence of it to us now. And, if not, then that means we're never going to obtain that knowledge or nobody in our future deems it important enough to return to recent times and before to prevent atrocities, give us the cure for cancer or even a nudge towards developing the time travel technology for ourselves. Unless human behaviour changes a drastic amount between now and then, I can't believe there won't be at least one person who would achieve this and, if just one person did, common sense tells me that we would know about it.
Perhaps one day, science will give us an answer for sure but for now it seems that nature has provided a barrier that allows time to only flow one way, albeit at varying rates. No other evidence so far supports any other hypothesis and commoon sense agrees for now..but time will, or maybe won't, tell.