I also believe it is possible, but not until we can develop more powerful energy sources such as nuclear fusion or matter-antimatter reactors. All of my (and other peoples)ideas require massive amounts of energy for their faster than light drives. As relativity states that FTL travel is impossible, the trick is to try and "fool" the Universe into thinking you are not traveling faster than light when you actually are.
1) Warp Drive (Star Trek). Works by compressing space in front of your ship and expanding it out behind. The result is that there is a gravitational gradient on your ship, and you "fall" towards the space in front. The thoery goes that you can compress and expand the space-time at faster than light speeds but when you are within the gradient (warp field) you never move faster than light relative to the local space-time within the gradient.
2) Worm Hole. This is a tunnel through space that links up any two points in the Universe so that thay overlap. If you pass through it you jump from one point to another. The problem with these are that quantum physics states that they are very unstable, and that passing anything through them will cause them to collapse, crushing what ever in in them.
3) Tachyon Converter Drive (my idea). A tachyon is a theoretical particle that travels faster than light, but will cease to exist if it moves below the speed of light. With my converter drive, the ship accelerates up to 99% the speed of light (that in its self is no easy feat), the tachyon coverter is switched on and it converts all of that atoms in the ship up to a tachyonic state. As tachyons only exist at faster that light speed, the ship then moves off at faster than light. My question is that are there tachyons?
4) Jumpgate (Babylon 5). This is a nice idea. You use a jumpgate to punch a hole in space which leads through to first-level hyperspace. When in this hyperspace, 1 meter of distance translates to many thousands of kilometers in normal space. Thus if you travel at say 1000 km/s in hyperspace, the equivalent velocity in normal space is well above the speed of light. Question is, just how do you punch a hole in space with a jumpgate? Also with this hyperspace, it is not hyper as in 4 dimensions instead if 3 but hyper as in a higher quantum energy level (a bit like energy levels in atoms except it applies to space)
5) Hyperdrive (Traditional sci-fi). This device works in a similar way to the Babylon 5. It punches a hole in space to step outside of the Universe into 4-dimensional hyperspace that lies "above" and "below". The speed of light here is much, much faster than in normal space so you can travel faster here.
So what are your ideas Spotty?