I own a Japanese Xbox 360, and have a lot of Japanese games. I'll list the decent ones (with their level of Japanese) here. If a multi-region game is listed here, it is the version released in Japan.

The shooting games all have English menus, or menus simple enough for language not to be a barrier if you're a beginner. The other games all have Japanese or English menus, depending on your Xbox 360's language setting (this is also how you change the voiceover language for some of them), although some of them only have Japanese menus. I put an asterisk next to games you might want to hold off on if you can't already read and write Japanese.

Shooting Games

Shooting Love, 200X
Raiden IV
Raiden Fighters Aces
Ketsui Kizuna Jigoku Tachi Extra
Mushihimesama Futari ver 1.5
DeathSmiles
Dodonpachi Dai-Ou-Jou Black Label Extra
Espgaluda 2

Japanese and English Voiceovers

Ninja Gaiden 2
No More Heroes: Eiyuutachi no Rakuen
Gears of War
Gears of War 2
Street Fighter IV
Super Street Fighter IV

Japanese Voiceovers Only

Way of the Samurai 3*
Halo Wars
Halo 3
Halo 3: ODST
Crackdown
Burnout Paradise: The Ultimate Box
Fallout 3*
End of Eternity*

English Voiceovers Only

Bayonetta
Ninja Blade
Ace Combat 6
F.E.A.R. 2
Tekken 6
Red Seeds Profile*

No Voiceovers (Text Only)

Project Gotham Racing 4
Banjo-Kazooie Nuts and Bolts

I have only two Japanese Xbox 360 games, but both are pretty good. They are:
1. Blue Dragon - This games is excellent for beginners who like RPGs.
2. Lost Odyssey - You need advanced Japanese to fully enjoy this RPG, but the Japanese version of the game comes with English/Japanese subtitles and audio if you start to feel discouraged.

I like the PS3 because it's multi-region. Although the ability to play American games is a temptation from my studies.