"But if we now imagine bodies to be projected in the directions of lines parallel to the horizon from greater heights, as of 5, 10, 100, 1000, or more miles, ... those bodies, according to their different velocity, and the different force of gravity in different heights, will describe arcs either concentric with the earth, or variously eccentric, and go on revolving through the heavens in those orbits just as the planets do in their orbits."One of the frequently recurring schemes in nanotechnology-in-space discussions is the skyhook or synchronous orbital tower. If such a structure could be built at all it would almost certainly require molecular manufacturing capability. The reason is simple: the structure would require at least ten thousand, and more likely 100 thousand, tonnes of near-atomically-perfect buckytubes or other graphite cable in a tapered form on the order of 80 thousand kilometers long.
--Isaac Newton (writing in 1686)
The theory behind the skyhook makes clear a number of other difficulties besides merely fabricating its material: It is essentially a satellite placed in geosynchronous (GEO) orbit, long enough on one end to reach the ground, and on the other to balance the ground arm and keep the center of mass in GEO. Among other things, you have to get it up there somehow. It has to be near the equator. It will get hit, ultimately, by almost any satellite not in GEO, meaning it is essentially mutually exclusive with satellites. And the stationary skyhook is among the more sedate of the blue-sky earth-to-orbit schemes, with a respectable intellectual history and numerous references and analyses in the literature.
A more practical scheme would likely be something that was marginally possible with current technology. It is difficult to find new ideas in the area, since so many have been proposed for so long. However, here is one which I have not heard of before; this may be its first time in print.
Build a structure 100 kilometers tall and 300 kilometers long. Put a
linear induction (or other electromagnetic) motor along the top. An elevator
goes straight up 100 kilometers to the starting end. Payloads are then
accelerated horizontally into orbit with an acceleration of only 10 G's
(which appropriately cushioned humans can stand for the 80 seconds required).
This hybrid approach overcomes the drawbacks of both the typical orbital
tower schemes (it's less than 1% the height of a skyhook) and electrolaunch
ones (air resistance at 100 km is a million times less than at sea level).
Once the tower is in place, it would be practical to launch other accelerators
(in pieces) to orbit. An orbital accelerator would have the advantage of
low rendezvous velocities, and the disadvantage of needing to fire something
backwards periodically to maintain its orbit. It could be much longer than
the tower and thus could form a second stage capable of launching humans
on transplanetary trajectories at survivable accelerations.
Skyhooks with nanotechnology
Electromagnetic mass driver "kit" (plans) can be had from SSI
NASA nanotechnology applications
NASA's maglev launch prototype
JPL electromagnetic launch page
JPL skyhook page has a brief discussion of "ultra-tall towers".
Robert Bradbury's mass driver references