Online Chess Kingdoms
First off, to even consider this game, you have to at least enjoy chess on some level. If you remember the old Battle Chess games of the past where the chess pieces come alive and fight each other after a move is made, Online Chess Kingdoms closely resembles this and does a good job of expanding it. It is still primarily a chess game however so be aware.
Online Chess Kingdoms offers five different unique chess sets and two different modes of play, classic quick match and story mode. The story mode adds some incentive and goals to just playing one game after another as you conquer other kingdoms through chess games and the five chess sets help keep the game fresh. In addition, the AI is well designed to allow novices and experts to both get a good challenge without getting frustrated or blowing out the AI.
Graphically, there isn't much to say except there's enough detail to keep the game interesting. In addition, the audio is rather sparse but it is a chess game so it didn't feel like there should have been more.
Although this type of game would never survive on a console, it fits well on a portable system. If you like the occasional game of chess or idolize Bobby Fischer, Online Chess Kingdoms will probably be welcomed on your PSP.