Lumines is a great puzzle game in the tradition of Tetris. Not only is it really fun in single player, it's truly addictive in multiplayer as well!
First off, the game itself. It's just like tetris, where blocks fall and you arrange them. In this case, they are all squares, with two colors. You are trying to make the colors connect up into blocks. There is all sorts of different color changes, music changes and cool techniques you learn as you go. Don't just play it a few times. Keep playing up into the higher levels, and it becomes a truly amazing game.
Then you can take it multi-player, and the head to head gameplay is really fun. It's not just "two people building side by side towers" like most other game systems. You actually use the same board and slide the ownership of area back and forth based on how well you do. It is incredibly fun!
There are other challenges, with puzzles and time trials, but the basic game is really the core here. It's perfect for picking up for 15 minutes when you're waiting in line - or it can make an hour long train ride zip by in seconds. This is really the must-have game for your PSP!
Buy Lumines from Amazon.com