Starting June 17th and running until August 5, AMC will be having $1 movies every Wednesday at 10 AM. Find out more details and a participating theater HERE. The only AMC I could find in Utah was in Layton. But you can check your local area at this website as well.
Don't forget, Cinemark is doing a movie club as well. They are 10 movies for $5.00 or $1.00/movie at the box office. The list is now up at this link of what movies your local theater is showing.