I would have to say reading a book is a form of time travel for me. I can get so caught up in a book I lose all sense of where I am, and I feel transported to another place and time. It's like I stepped through a door and am in another dimension! Some movies are that way, too. When I recently saw The Hunger Games, it was like I was right there living it with Katniss and Peeta.
Good novelists want it that way. They want to make their literary creations come alive for their readers. In a way, it's time travel.
I have to say I like mwalter's view. People can time travel everyday (through literature and film). People are also able to look online and see how life was "way back when." As for the possibility of time travel, I would think that cryogenic freezing would be a plausible option (not saying that it is something which could be an actuality).
If the term "time travel" doesn't have to be taken literally, then I'd say reading is a form of time travel. Authors usually write for their contemporary audiences, so they reflect the values and attitudes of the time in which they were writing, which may be significantly different than our own.
Perhaps a way to "kind of" time travel is to pursue cryogenic freezing. If a person were to be frozen alive and preserved for hundreds of years, he/she would wake up to a new time.
This is not time travel properly speaking, but it is a way for one person to potentially live in multiple time contexts.
This is a topic that has always fascinated me, though I'll confess that I'm very much a layman. Another way, in addition to the faster than light method, has been proposed by some physicists. It is based on travel through wormholes, portals through spacetime that have been predicted by, or at least are not inconsistent with, general relativity. The idea is that one would enter a wormhole, then "come out" the other end at another point in spacetime. The limitation is that a person travelling through a time travel machine based on a wormhole could not travel back to a point in time before the machine was developed.