Metal Gear Solid for Game Boy Colour. I don't remember a whole lot of the plot but it probably is a decent entry to Snake's world.
Holy crap, Phoenix Wright: Ace Attorney was the first game I completed in full, I have since completed other games years after I purchased them, but Phoenix Wright gave me a reason to keep playing, even though it was getting emotionally intense. The Miles Edgeworth being accused of murder case was TIGHT.
Valkyria Chronicles is one of the better J-RPG plots I have seen, but Final Fantasy IV was the first Final Fantasy game I truly "played", I still haven't finished it, but when the knight dude Cecil or whoever accidentally burns down a village with the king's item, that was epic, that was something that made me say "You finally did it, damn you. You blew it up! DAMN YOU ALL TO HELL!" in a Charleston Heston voice.
The World Ends With You has a pretty oddball plot for a Square Enix game, first ever skinny androgynous protagonist I've seen in a Square Enix game which is only tortured emotionally by modern emo standards, not "My entire family was killed and nobody loves me" standards. Neku feels like a more real kind of angsty teen, rather than an angsty manchild who wishes he was still a teen such as Cloud. Neku is redeemable and probably has problems which are mainly with Japan's societal structure rather than with human beings like he thinks he has problems with.