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NASA has had a Centennial Challenge open in power beaming for some years now. From :

This challenge is a practical demonstration of wireless power transmission. Practical systems employing power beaming would have a wide range of applications from lunar rovers and space propulsion systems to airships above the Earth. Another future application of power beaming would be the space elevator concept.

In 2009 the competitors drove their laser-powered devices up a cable one kilometer high, suspended from a helicopter, and LaserMotive LLC was awarded $900,000.

It turns out that it is really tough and actually somewhat dangerous to have a helicopter dangle a 1 km string perfectly vertical. This also "doesn't scale" (i.e., there is no way a helicopter is going to dangle a 5 km string for a longer test), and future competitions will be done horizontally, on the ground. (This also fits in with the idea of power beaming to rovers, say one exploring the always dark Shackleton Crater at the Lunar South pole, which is frankly a more realistic near-term prospect than a terrestrial space elevator.)

I believe there is still $ 2 million (USD) to be awarded, so slashdotters should get to it and go out there and take the Governments money.

I can think of one http://www.spaceelevatorgames.org/

Check out the web site for the space elevator competition. It includes videos of climb attempts, and lots of data about what they're trying to accomplish and why.