Here is a fun app that lets you design and play your own games. Infinite Arcade by Tinybop is an iOS app that lets you make platformer, adventure, and pinball games. You can choose from the characters available or customize your own. It is possible to add words, clues, and secret messages for your characters.
Infinite Arcade lets you save and play your own games. You can create levels with obstacles, enemies, and hazards just how you want. The app is available for under $3 at this time.