The iCampusPrize at MIT does exactly that. It has $15,000 in prizes and it has been running since 2008. It has two stages: (1) for prototype submissions and sm

The iCampusPrize at MIT does exactly that. It has $15,000 in prizes and it has been running since 2008. It has two stages: (1) for prototype submissions and small prizes of ~$1,000, (2) final fully-working submissions and big prize of up to $10,000. We entered the competition in 2011 with a book exchange site and won ~3,000. The site's still running. Past winners: http://icampusprize.mit.edu/past-winners/ http://icampusprize.mit.edu/past-winners/ Edit: fixed wrong link