Is time travel possible??
Unfortunately, No but somehow yes!. See below
Time travel refers to travelling to past or future in time dimension.
As stated in answer above "...but somehow yes..", time travel actually is possible.
All you need to do is to not do anything. You are already travelling in time to future but at a relatively almost same rate with respect to everyone around us on our planet. So, we don't experience it.
According to Einstein's relativity, if you somehow manage to move at a speed faster than "speed of light", you'll be travelling in time in backward direction or say in past. May be in future as well. But unfortunately that doesn't make what we generally call "time travel" possible because cosmic speed limit is "c" it self. If you move at speed of light, the term "time" would seem imaginary to you i.e; you'll not experience time.
However, Einstein's equation predict that if you velocity increases, your mass does the same. So, it becomes impossible for a body with mass to reach speed of light.
The region in space around a mass has curved space-time, time actually goes on slower in that region but to make really big time dilation effects, corresponding masses are needed as well. This is the reason why clock of satellites are synchronised to work at different rate. Obviously, you would see more effects near black hole.
Some people think that wormhole can't help you travel in past amd future in time, but the real version is slightly different.
Spacetime is curved, to move across two points in curved space, the curve adds up to increase your distance. Wormholes are shortest distance between two points. So, though you might go slower than "c" still you would reach faster. However, wormholes are just hypothesis and only a part of science fiction but yet they are possible.
Einstein's relativity suggests that if universe was spinning there would be time loops all around. But unfortunately our universe isn't spinning.
Now, coming to the answer you want. "Time travel" being possible or not depends on what you think it to be. You are already travelling in time, relative to other objects like say a space shuttle. But if time travel is only limited to going in your past or future, perhaps it is a superstitious fantasy..