Recs.
Updated
Super Mario Run is the first Mario game made specifically for mobile play. It's an auto-runner, meaning you can't control when or which direction Mario moves, but you exchange that ability for the ability to jump by tapping the screen, and it comes with a bevy of elegant mechanics.
Super Mario Run is currently exclusive to iOS, but has an Android release scheduled some time in March 2017.
Specs
Pros
Pro Automatically mobility accessible.
Because the one button is out of the way and reachable with either holding position, and still easy to use with the phone in a holder and pressing with another finger or pointing device, the game doesn't need any kind of modification or special controller to be accessible.
Pro It's a challenging game that's very addictive
As with any Mario game - you want to collect as many coins as possible. If you collect them all within one run, then a new, purple set of coins appears in harder to reach places. If you manage to get all of those, then a third set appears. It's incredibly addictive and will constantly put your skills to the test.