Philosophy
We've been talking your ear off about how cool the speed of light is the ultimate limit, which can never be broken. Let's revisit this issue from a non-mathematical point of view.
Approaching the speed of light forces time to slow down, and this is how we can travel to the future.
If a twin decides to go space-gallivanting and takes off in The Albertian, he might become younger than his twin. The math tells us that after traveling at a speed of 0.5c for 5 years, 7.5 years will have passed on Earth, where his now, younger twin remained. The Earth twin will be 2.5 years older than the astronaut-twin.
It's more complicated to calculate an exact time dilation effect with general relativity, but the idea is the same. If the Earth twin decides to get even and takes a turn in space around a black hole for a while and then returns to Earth, he'll be the youngest twin once again. Cosmetic companies promoting eternal youth just might be joining forces with modern physics in the next century.
We experience this kind of time dilation every day while driving, jogging or biking, but since we are moving at speeds much less than c, time dilation doesn't occur at a noticeable level.
Having this upper limit on velocity implies no information can be relayed faster than c. It takes eight minutes for a sunray to reach Earth. If the Sun exploded, we wouldn't know until eight minutes had passed. When we look up at stars at night, we see them as they were thousands and even millions of years ago. Entire star systems could've died and been reborn and we wouldn't even know. We'd just blissfully gaze up at the stars and try to impress our date for the night by pointing out all these neat facts.
There are other ramifications to the speed limit, too.
If we ever detected a signal coming from an advanced alien civilization, chances are the civilization would already be long gone by the time their greeting ever reached us. Even traveling at the speed of light, cosmic distances are just too great. It could be bad luck. Or it could be that perhaps we simply aren't meant to communicate with other intelligent life forms. Earth seems to have enough problems already dealing with its own species.
Or maybe we are meant to break the barrier of light speed, in spite of the fact that, according to special relativity, we'd need an infinite amount of force or energy to accelerate an infinite mass. Other ways have been suggested, such as equipping spaceships with warp drives and cutting through the fabric of space-time by building wormholes.
Since information travels at the speed of light, going faster than c would allow us to get our hands on that information before it reached us. We could in theory change the course of things and set up a new future. In other words, we could travel into the past.
This would imply the possibility of paradoxes. Let's say both twins go back in time. Their great-great grandfather, Lord Thomas Cobb, invites them out on a hunt around his palace grounds. They accidentally shoot him while trying to kill a animal on the endangered species list in their own time. Doesn't the death of Lord Thomas Cobb imply they were never born?
Perhaps there's a reason we can't go faster than the speed of light. It guarantees a continuous flow of time where causality can never be broken.