I've had a go at solving the [Eternity puzzle](http://en.wikipedia.org/wiki/Eternity_puzzle) (1,000,000 GBP prize) and [Netflix Prize](http://www.netflixprize.com/) ($1,000,000) in the past. I didn't win either, but they motivated me to find out about a new area. 

What other contests with prizes do you know about / have competed in yourself?