In the name of saying something which hasn't been done to death, let me skip to my personal favies. I love these games to death, but they're not that popular among vintage gamers.
Parasite Eve: Action horror RPG. Great soundtrack, visuals, and the one story about evolution I actually approve of. Not to spoil too much, but a particular location you briefly visit near the beginning of the game becomes my favorite dungeon of all time at the end.
Parasite Eve 2 : Tank controls done right. The M4A1 is an awesome weapon that you can put all sorts of attachments on. It's nice to play a survival-horror game where the bayonet is actually a valid weapon, even compared to a laser or grenade launcher. Again, good cinematography and phenomenal gameplay, but the story's kind of a notch down from the first one.
Mandatory footnote: PE2 has a really long learning curve.
Tenchu 2: Sick of Naruto? Want to see ninjas actually act ninja-like? Look no further.