Space Elevator

Arthur C. Clarke proposed the idea in his 1978 book Fountains of Paradise — build a 50km tower on Earth near the equator, put a big mass (like a tamed asteroid) into geosynchronous orbit, and connect the two with a massive cable. The whole assembly stays upright, essentially attached to space itself. Run electromagnetic elevators up and down the cable, and you can lift payloads or people into space for a fraction the cost of rockets or shuttles. Amazingly, NASA is now taking the idea seriously, although the idea is going to take a while to get off the ground (think late 21st century).