If you’re enrolled in a law school or other graduate school program in the U.S., check out the Pacific Legal Foundation “Judicial Awareness Writing Competition.”
Participants can write on one of three questions to win $5,000 for first place, $3,000 for first runner-up, or $1,500 for second runner-up. (I won an essay contest when I was an undergraduate and the $1,500 — a lot of money back then — kept me from having to drop out of school for lack of funds, so I highly recommend the idea.)