Here's my small yet AMAZING list (note the majority have some kind of problem but if you get pass that you will LOVE IT)
The World Ends With You (absolutley amazing game, for me it's the best DS game in existence)
Last Remnant (XBOX 360, for some reason didn't get good reviews and had no commerical awarness it's hidden but you can easily lose 50+ hours with just the sidequests, great story, etc)
Drakengard 1 & 2 PS2(also SE hidden game but a really addictive one, the second one is way better but i suggest playing the first one to see the badass pro.)
Star Ocean, Till the end of time and new hope PS2-XBOX 360(really immersive gameplay wise, that's if you don't mind semi-unintresting characters, and long intro)
Shinobido Way of the Ninja PS2(amazing ninja game, good graphics, nice ragdoll physics, and one of the best stealth games ever, oh you get to controll the ongoing war with your actions so make sure not to get seen!)
Way of the samurai 1 & 2 PS2(amazing and utterly the BEST samurai game i have ever played, same guys from shinobido, but just generally better in everything, once again you controll your the war thus your destiny, oh i personally like the first a little bit more than the second)