Zillions of Games is a General Game Playing system that plays chess. It was perhaps designed with chess specifically in mind, but in order for the program to play a game, you must first load a zdf file which specifies how the pieces move and what the goal is. It can also play checkers, go, shogi, etc.
The engine Nebiyu running in the GUI Winboard Alien Edition can play Checkerscheckers, chess, go, reversi, Amazons and a few other games. On Android, there is a program called XO Demo which plays many board games. On iOS, there is an app called Social Games.
The Association for Advancement of Artificial Intelligence holds a General Game Playing competition every year at its annual conference. All The programs are designed to play almost any game, and are not told in advance which games will be played. Each of the programs could theoretically play chess if someone wrote up a rule set. I don't think the GGP competitions have ever included a chess event however. The authors of Maligne (Universityas one of Alberta) have written a paper on feature learningthe games however.
In the context of chess engines, the word "learning" refers to the engine adapting its opening book (book leaning) or evaluation (automated tuning) based on its results. Many engines learn in this sense, eg. Crafty, Deep Thought, Exchess, Gaviota, Junior, MChess, Neurochess, Romichess orand Tao.