It has been confirmed that there will be mini-games the player can play in Legends of Equestria.
During the August 2012 livestream, there was a video of a Pacman-like minigame called "Pony muncher" where the player moves a circle with the words "om nom nom" written on it to overrun cupcakes and cookies. There is also the rumored cloud Tetris game, but it isn't confirmed yet.
The Pac-Man game was the only mini game that could be played during the pre-alpha stress tests. It was accessed through the Ponydale Well.
During a livestream, Swebow, the game's creator/current head of project, showcased called "Ponyville-Pegisi Race!" A racing game where the Pegasus player would race to compete for the best time as they go through hoops. It is unknown how the other races would play this mini game.