Snatcher (by Hideo Kojima of Metal Gear Solid fame) is one of the best. Basically a Blade Runner-esque adventure/detective game with a bit of action too.
I started that one and it was actually pretty fun before my emu or something started bugging out.
Eventually I'll sit down and watch a let's play or find a good copy.
Lunar: The Silver Star and Lunar: Eternal Blue were great.
Dark Wizard! It remains one of my favorite games of all time and was [probably too] far ahead of its time. It's an open-world turn based battle strategy game with leveling units, multiple storylines to play through (with distinct heroes, persistent/leveling units, skill trees, evolution trees, etc), lots of secrets, and so on. It also has some great orchestral type music [1].