As far as older titles go, I've always liked Bomberman in spite of the fact that I really, really, suck at this game. I'm not sure what it is about the strange alchemical creation of a small Japanese character running around setting bombs that enthralls, but man, is it fun.
Bomberman for the PSP recreates the classic gameplay almost perfectly, going so far as to offer an unlockable classic mode. The classic mode is nothing but an updated version of the original Bomberman. All told, including classic mode, I think there's about 150 different levels you can play through. In addition to Normal, Arcade, and Classic modes, you can share the game over the PSP's wireless connection to play versus games with your friends, even if they don't have a copy.
My favorite mode is probably the normal mode. As you play through 10 worlds with several levels each, you'll collect various powerups that you can store in an inventory. When you need to use the items, they'll be there for you to expend, allowing you to progress carefully through the first few levels, and then later bust out some of your more powerful items to take on difficult enemies in a later part of the game.
Graphically, aurally, in all manner of presentation, Bomberman isn't anything to write home about. The good news is that it really doesn't have to be. Bomberman isn't over complicated with a new look, unlike some other titles I could name, and the only real complaint I had is that sometimes the level color palettes can be a bit garish.
In the end, this game is great to have if you like playing Bomberman, or have a bunch of friends that do. It is still a little too expensive for my tastes though, as Bomberman still doesn't have that wide appeal that's going to make it a good buy for everyone.