A free app for Android, by R-Soft LLC.
If you are looking for a game you can play with real people online, with no sign-up, login, or registration, then you should play Backgammon Online.
Backgammon is a classic board game for two players, where the object is to get all of your checkers to the other side of the board before your opponent.
To play, you need to place your checkers on the board. Each player starts with several pieces, and each piece can move one space in any direction. As you play, you will roll dice and move the checkers to get them to the other side of the board.