Even though a game might be playable without knowing anything about Japanese, it doesn't mean it will be enjoyable.
I used to play Japanese games without any Japanese knowledge, and they were all easy fighters and the like. However, one I learned Japanese and started playing Japanese games again, it was so very much better.
So, if you want to play Japanese games badly, I'd recommend Jump! Ultimate Stars. Excellent game. Also, you can play Osu! Tatakae! Ouendan! It's a rhythm game like Elite Beat Agents... but better.
Basically just try to stay away from RPGs unless they have a menu translation patch. I tried to loan my friend my DS to play FF4, but he had a lot of problems with not being able to remember what attacks looked like written in Japanese, and ended up having to wait for the patch (or me to stand over his shoulder and tell him what everything means).
Also, many of the games Japan gets will eventually be brought over to English. And of those that aren't, the really popular ones will have patches available on the net (check these forums) for the game.
So, good luck on your quest to find good Japanese games!