Is time travel possible? Time travel -- often featured in movies, books, or facetiously in conversation. There are also theories treating time as simply another dimension, which to the layperson might imply forward and backward movement is possible at will.
But what do we know scientifically with respect to the possibility or impossibility of controlled time travel? Are there any testable theories on the horizon that may support or eliminate controlled time travel as a possibility?
By "controlled time travel" I mean the ability to willingly transport a complex object or being through time (perhaps only to the past, or a copy of the past, which would be an answer too).
 A: Well, this is a migrated question and it deserves an answer from a physicist.
In my opinion, within the physics framework we have developed up to now, i.e. the totality of the accumulated theories which are based on experimental results, time travel in the sense of a human controlling his/her position in time as one can control it in space, is not possible.
Of course theories change and evolve, so this is the present answer. If, as @Luke in the comment said, a proven time traveler had appeared, that would have been experimental evidence that would have forced a change in theories.
The only traveling we do in time is from the present to the future, willy nilly.
A: You can travel to the future by accelerating near the speed of the light. 

In physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth.

Source: http://en.wikipedia.org/wiki/Twin_paradox
Wikipedia discusses various theoretical possibilities for backward time traveling, which include by walking near high density cosmic masses, such as black holes that deform the space-time fabric, in a particular direction.

Residing just outside of the event horizon of a black hole, or sufficiently near an object whose mass or density causes the gravitational time dilation near it to be larger than the time dilation factor on Earth.

Source: http://en.wikipedia.org/wiki/Time_travel
A: UPDATE:
In the following analogy I have failed to take into account the Relativistic Doppler Effect which would cause "me" to age more slowly than "you". Since the speed of light is said to be independent of the motion of the observer the Doppler Effect, which may imply the opposite, is hard to accept.
The problem I have may lie in my idea of what "independent of the motion of the observer" means. But I digress...


Disclaimer: Someone else may want to
  expand on this in a more formal,
  correct, and scientific answer; but
  here is my layman's idea of
  theoretical time travel (well,
  technically what i'm describing is
  time dilation). It is probably wrong
  but this "understanding" appeases my
  curious brain.


Light is tricky. And relative. It "travels" at a constant speed (180000 mi/s) relative to the OBSERVER.
Here is my home-brewed analogy on the strangeness of light.
Lets just pretend that light moves at 10 miles per hour (or km/h if that's your thing) for simplicity's sake (I have a hard time comprehending just how fast 186000 mi/s really is).
If I'm driving my car toward you, with my lights on, at the speed of light1 (10 mph) how fast would the the light from my headlights be moving toward you? 20 mph, right? That would make sense...but it is not the case. The light from my headlights would travel at the constant 10 mph - relative to your perspective.
Now, relative to my speed (10 mph), at what speed would I perceive the light moving away from my car? 10 mph.
Hey, its light... it can do whatever it wants!
Now, I'm going to drive right on past you at my speedy 10 mph. And lets say instead of tail lights I've got a big digital clock shining back at you (its a 24-hour clock, where 00:00 = 12:00AM). Tick Tock. You never want to be late and don't want to rely on my clock so you have your own just to make sure mine is correct at all times.
Okay, think about that.
Tick Tock... I'm now 10 miles away from you still travelling at the speed of light. The hour hand on my clock changes from 00:00 to 01:00. The light zooms toward you at 10 mph. Meanwhile, I'm still driving away from you. Another hour passes for me and my clock changes again from 01:00 to 02:00; I am now 20 miles away. At that exact moment you perceive that first change from 00 to 01. Now you think to yourself, "Man, his clock must be slow!!! Its an hour off according to my clock!" Your clock says it is 02:00 (and so does mine, but you haven't perceived that yet).
So you wait another hour and look back up at my clock expecting a change. But nothing happens. You wait another hour and BAM, my clock finally changes from 01:00 to 02:00. But it is now 04:00 on your clock (it's 04:00 on mine too, but again... you haven't perceived that yet).
I suddenly and instantaneously turn around (impossible, yes; but I'm traveling at the speed of light so I'll do what I want). I'm coming towards you at 10 mph. My light (which beaming back at you telling you it is 04:00), from your perspective, is also traveling at you at 10mph. Since I am 40 miles away it should take me, and my "04:00" light, 4 hours to get back to you. So, 4 hours later, when you see my "04:00" light, I'll show up.
So, I appeared to either have a slow clock, or be 4 hours in the past (or 4 hours younger depending on how you look at it).
Here's the catch. If I had been monitoring your clock I would have witnessed the same time dilation. Your clock would have appeared to be slow and you would have appeared to be moving through time more slowly than me. (That's the "relativity" thing kicking in)
Here is brain thumper: what if I could go faster than the speed of light2?
So, it is not really time travel... but it is about as close as we are going to get until we figure out those darned wormholes3. :-p

[1] Einstein pretty much said we can't really travel at the speed of light under our current understanding of physics. (This kid may have something to say on the matter, though.)
[2] AKA "FTL" according to Stargate
[3] AKA "Hyperdrive".

So, about wormholes: If we could travel to the other side of the universe and then look back on ourselves the light we would see would be from a long long time ago (in a galaxy far far away).
What if we got in our super-speedy FTL spaceship after having been instantly transported via wormhole to the other side of the universe? Could we show up back on earth before we left?
A: The real problem is whether it's possible to move back in time (we all move forward in time)
Our whole understanding of the world is based on basic concepts, one of the is causality
causality is a property of our mind (not the physical world) - we believe that one event causes a second event when some conditions hold.
The causality links events such the cause preceded the effect
(this a very brief and partial definition of causality, but it should be enough to make the point)
So a visitor from the future is like a ghost, or other paranormal phenomena


*

*We'll either find a different explanation, which is consistent with the basic ways our mind works

*We'll ignore it 
So even if time travel is physically possible, we won't interpret it's implications as time travel,
So our mind (and science, which is a product of our mind) wont be able to  
