So Einstein said that nothing can travel faster than the speed of light, and in fact getting anything going at any relativistic speed at all isn't feasible. So what? There are ways of getting around this. The real trick to moving something faster than light speed is to remember that "velocity" is just the distance traveled divided by how long it took to travel there.

• Warping Space: As seen in Star Trek as warp drive. Ever been on a long car trip through many small towns, or roads you know are infested with highway patrolmen, and wished that the road would just get shorter since you can't go any faster? That somehow a mile would only be half as long? That's exactly what warping space does. You make the space in front of you "smaller" than it actually is (possibly using a gravity field), thus increasing how much distance you cover without actually increasing your speed. For example, if one could warp space in front of one's car by 10%, a mile would only be 4752 feet long, and a car travelling at 50 miles per hour would cover a little over 55 miles in an hour. Hence, you could travel 186,001 miles per second without pushing your speed above 169,092 miles per second.

• Folding Space: As seen in the book A Wrinkle in Time in the form of the tesseract. Madeleine L'Engle explains folding space in the book by imagining a string stretched between your fingers. Now imagine that there's an ant at one finger who wishes to get to your other finger, so he is going to have to walk all the way across the string. It would certainly make the ant's job much simpler if you'd just bring your two fingers together, now wouldn't it? Of course, space is a bit more complicated than that, and you can't just ask someone to fold it for you. An immense gravitational force might be enough to fold space like this, though the energy requirements would be astronomical, and by some estimates, exceed the total ammount of energy knowt to exist in the universe. Travel would be instantaneous, so you could travel the entire span of the universe in no time at all, with an effectively infinite speed.

• Tunneling Through Space: As seen in the movie Event Horizon as the thing that sent a ship full of folks to Hell somehow, in Deep Space Nine as a quick way to piss off the Cardassians, and in Contact as the thing that aided Jodie Foster's breasts to a zero-gravity perkiness. Also known as wormhole, or Einstein-Rosen Bridge travel. As Sam Neil stated in EH, the shortest distance between two points is not a straight line, but zero. He illustrated the point by drawing two points on a piece of paper, folding the paper so that the points were in the same spot, and then poking his pencil through the paper. At first glance, space tunneling looks just like space folding; however, space tunneling does not fold space. It bridges two separate points in space by poking a hole in the fabric of space itself. You go in one hole, and instantly emerge at the other one, like the playing field in "Asteroids." (actually, that's a torus, but you get the idea) Black holes are thought to create these "pokes" in space. They could be used to move something faster than the speed of light, if only they weren't unstable and didn't immediately crush you to maximum density as soon as you got past the accretion disk, not to mention the fact that we have no idea if they open up anywhere. A wormhole, more or less, would be a stable black hole that opened up somewhere else and didn't crush you. Again, travel would be as close to instantaneous as makes no difference.
• Hyperspace: As seen in Star Wars as the hyperdrive, a rarely working feature on the Millenium Falcon. Imagine playing with toy cars on an old, warped, gritty table, where the cars are hard to slide back and forth. The cars can't really get going very fast at all. It's much faster to pick them up to move them from place to place, but to pretend like they're still cars, you hold them up just a little ways from the table, so they can still interact with whatever else you're playing with. A hyper-space is a space that is somehow above or beyond "real" space. Anyhow, the idea is that travel in a hyperspace is somehow shorter than in real space; either time goes slower, or distance is shorter, or maybe both. You go into hyperspace at one point, travel a ways, and drop out of hyperspace quite a long ways farther along in real space than you flew in hyperspace. When you picked up the toy car, you moved it through a hyperspace (the space above the table, to be specific). There was no old table to worry about, just like there would be no physical world to worry about in hyperspace. Still, you had to keep interacting with your play world, so you didn't pick the car up too far. Moving into a hyperspace would be really hard to do, and you couldn't get too far away from real space or you might not be able to find your way back; it would be like going out to sea on a foggy night without a compass. So when you hit hyperspace, you haven't really left this dimension. There's still an "echo" of you in real space, and there are "echoes" of real things in hyperspace. Speeds through hyperspace would be like speeds through warped space, with your apparent speedup being determined by how much faster hyperspace was than real space.
Right then! So now that we all know how to move something faster than the speed of light, I want to see you people devising ways of doing this by the end of the century. Bloody hell, it's almost 2002 and we have yet to send something alive to Mars. Makes me weep for the future...
All content for this node (minus the smart-ass asides about Jodie Foster) courtesy of Prof. Benjamin Blackhawk's "Let's Get Hyper(spaced)!" summer course, which I took eight years ago. I've never seen the world the same way since.