Feasibility of a skyhook - space elevator?

A space elevator is a proposed non-rocket spacelaunch structure (a structure designed to transport material from a celestial body's surface into space). Many elevator variants have been suggested, all of which involve travelling along a fixed structure instead of using rocket-powered space launch, most often a cable that reaches from the surface of the Earth on or near the equator to geostationary orbit (GSO) and a counterweight outside of the geostationary orbit.