h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Kim Stanley Robinson's trilogy has an interesting take on the space elevator. They exist both on Earth and Mars by the second book. The description of what would happen if the orbit of the elevator decayed is fascinating, basically Mars ends up with a crashed cable that encircles the planet several times, leaving almost a *canal* of the Lowell type. Well worth the read for that alone, but his sociopolitical insights are good as well.

The really interesting thing about a space elevator on Mars is that the geostationary point is higher than the orbit of one of the moons (Phobos). You could move the moon before building the elevator, but a more exciting prospect is to vibrate the elevator so that it swings from side to side like a vibrating string on a guitar, with fixed ends. You'd have to time the period so that is was always out of the way when Phobos was hurtling past.