I've always found the idea of a space elevator a bit outlandish. Basically the idea is that we lash a piece of cable to a large space object in a geostationary orbit, then lash the other end to a spot on the Earth. Now that you have your cable to space, you can take an elevator to space!
Of course, the cable would have to be 10s of thousands of miles long, without slack, super strong, and attached to an object in perfect step with the rotation of the Earth and the additional force added by the elevator and payload as it climbed into orbit would have to be compensated for. I just don't see it, but others do, and now they are suggesting that carbon nanotubes could be usefull as the cable. Here is the story.