In an X PRIZE Foundation blog entry, Tom Vander Ark asks "why use prizes"? He also asks "when are prizes useful"? Of course he answers the questions, too. The short answer to the first question is
There are three primary benefits of well constructed prizes and media savvy global competitions; they are a high leverage and efficient investment, a powerful innovation strategy, and an effective change strategy.
He expands in detail on all 3 points. He also gives a detailed answer to the second question using various example prizes covered on this blog to make his points.
One interesting bit of information about the Google Lunar X PRIZE is used:
A prize attracts teams from around the world, across boundaries (e.g., more than 260 Google Lunar X PRIZE registration requests for GLXP from 35 countries).