I've been hearing rumours that the technology is available for the last couple of months/years, but last weekend I read on Slashdot that people are actually going to build it: Arthur C. Clarke's Space Elevator. Wow. I mean two times wow. First wow: after predicting the telecommunication satellite, Mr. Clarke seems to have done it again with the Space Elevator in his book Fountains of Paradise. Second wow: when I read the book some 10 years ago, I thought "such an elevator would come in really handy". And now they actually seem to be going to build it. The first step is apparently making a manufacturing plant for the cables.
In answer to the question "what the heck does one need a space elevator for" (like my fiancee asked yesterday, not quite sharing my enthousiasm): it would allow us to haul up loads (like stuff for the International Space Station, new sattelites, ...) into a geosyncronous orbit. By comparison: the Ariana 5 ECA can lift 10 tonnes to geosync orbit. Let's for a moment assume that the Space Elevator can lift 10 tonnes per day. Imagine what a burden on the environment a launch each day would mean.
And if we go on to equip the top station of the Space Elevator with a launch pad, we'd have an ultra-efficient launch station too: rockets would need far less fuel to get away from earth if they start at a hight of 36 000 km rather than on earth. The sky is the limit! Well, space actually ;-)
Edit: according to LiftPort, the group who are mentioned on Slashdot, the "inventor" of the Space Elevator was actually Yuri Artsutanov, who wrote about it in Pravda as early as 1960.