You'll have to find a used game if you want it under $20. These are often in great shape-- i found an awesome old game for $3, yes really, and It works perfectly. Gamestop has tons of old games.
Off the top of my head, Endless Ocean is a cool game and it is $30.
Really, though, most $20 games that are new are total crap. It's a much better deal to buy used, and you'll be getting better quality too.