I am now owner of an Xbox 360 Premium...

But I've got only one game, Pro Evolution Soccer 6, which I plan to trade in at the nearest games store. Can anyone here give me reccommendations for great Xbox 360 games I could get?

Looking for some good J-RPGs or FPSs mainly.

I can help with the FPS recommendations. The Darkness and BioShock are both great single player games. For good Multiplayer online you'll need to wait a few weeks for something new, either Half-Life 2: The Orange Box or Halo 3 should work fine. Unless you want something more realistic, I have heard good things about Rainbow 6 Vegas.

Don't overlook Gears either, though technically it isn't a FPS, it plays like one and is excellent in both single & multiplayer.

If you're looking for a JRPG, check out Blue Dragon. Also, Eternal Sonata and Lost Odyssey are games you should keep your eye on for the future.

GRAW 1&2

The Darkness

Crackdown

Bioshock

Rainbow Six Vegas

Oblivion

Shooter: Bioshock

Racer: DiRT

Music/Rythym: Guitar Hero 2

Platformer/action: Kameo

Other: Crackdown

Multiplayer: Just wait for Halo 3