Promote your contests
When you do contests, make sure to promote them often in your own public communication channels.
Example is the ongoing twitch animation contest. The only public mention of it from Twitch has been a single blog post when it started. Most participants only heard of it via word of mouth. The purpose of contests like this is presumably to get attention to the creative section on twitch and attract more broadcasters and viewers. Then you should mention it on your blog and twitter accounts, make some press announcements, and regularly feature online streams of the participants as they're working on their entries. None of these measures would cost you anything.
Contests like these are good, and highly appreciated by artists. If the Twitch animation contest had been promoted more broadly it would have had many times the amount of participants and viewership it gathered, and twitch would have gotten far more value for their money.