Google needs a Google contest page to track their list of contests both past and present all in one place. They use contests in different ways (to get work for free, to train future employees, and to expose more people to their products).
Since I’m an optimist I try to imagine they do it mainly to encourage innovation and better solutions to the world’s problems both on and offline. Even if that’s not the whole story, it’s very feel good. It infuses a sense of fun and open-mindedness since they are always a bit quirky are aimed a broad age and range of people.
Contests can be a good way to get things done and you don’t have to fly people to company headquarters either. Guy Kawasaki got his book cover designed by running a contest.