You can require users to be following one or more accounts before they can enter your promotion. You can also filter users with no profile image and less than 10 followers (usually fake accounts.)
Have your users choose between 2 or more #hashtags, photos, videos, Twitter accounts.
Ask a trivia question and have the winner(s) picked from the people who answer it correctly.
Get feedback about a product or issue. Reward your users for their feedback.