David Smitherman of NASA/Marshall's Advanced Projects Office came out in 2000 with a project of space elevator, a long cable extending from our planet's surface into space with its center of mass at geostationary Earth orbit (GEO), 35,786 km in altitude. Electromagnetic vehicles traveling along the cable would transport people, payloads, and power between Earth and space.
According to Smitherman, construction is not feasible today but it could be toward the end of the 21st century.