Chessformer is free and simply must be played!
Chessformer comes from Nam Nguyen Sy.
From the App Store: Chessformer is a puzzle game . Having the best qualities of chess, Chessformer offers a grid-based board game experience using the familiar chess pieces you know and love. These pieces move as expected, but they fall down after moving and can't move again until they have stopped falling. The goal in each level is to capture the opposing king. But don't worry about losing your pieces to the king, who is lazy and never makes a move. Are you ready to be the latest chess prodigy?
There are 24 levels and I've done 23. Stuck on #24!
Seriously, Chessformer is FUN. Lots of 'aha' moments.
Other Chess Apps
Chessumo - point scoring game
Solitaire Chess - my favorite from this list
Board: Chess Puzzle
Mate in 3? Ok!
Chess Puzzle of the Day
Chess Light - very good
No More Kings
March Simple Chess