This is inspired by my friend Julien MARCEL, who has been posting about chess programs for iOS devices at TalkChess. I will attempt to cover chess programs for iOS devices (using Julien's TalkChess posts) and chess programs for Android devices.
The first program I will post about is the Android program I use and love:
Chess for Android (Free) : A computer chess GUI for Android devices created by Aart Bik.
From the description at Google Play:
Chess application (with UCI and XBoard engines support).
Chess for Android consists of a chess engine and a GUI. The application accepts moves through the touch screen, trackball, or keyboard (e2e4 pushes the king pawn, e1g1 castles king side, etc.). An optional "move coach" highlights valid user moves during input and last played engine move. Full game navigation buttons enable users to correct mistakes or analyze games. Games import and export as FEN/PGN to and from the clipboard, load and save as file, are set up through a position editor, or import as application/x-chess-pgn MIME type on startup. A draw by stalemate, insufficient material, the fifty move rule, or threefold repetition is recognized. The engine plays at various levels (including random, against itself in auto-play, or free-play, where the game can be used as a "magnetic chessboard"). The user can play either side and, independently, view the board from the perspective of white or black.
The application supports the Universal Chess Interface (UCI) and Chess Engine Communication Protocol (WinBoard and XBoard), which allows users to play against more powerful third party engines or even play tournaments between engines. Engine setup features pondering, infinite analysis, hash tables, multiple threads, endgame tablebases, and opening test suites.
The application contains a simple engine. Many other engines (Android versions of many UCI and Winboard engines) can be found at this link.
The author also has programs for checkers and Reversi (Othello).