Red Faction (PS1, PC) - Just one of my favorite series. One of the early FPS's with destructible environments. Continued with a series, RF 2, RF: Guerrilla, and RF: Armageddon. RF 1 and RF: Guerrilla are the best imo.
Indigo Prophecy, a.k.a. Fahrenheit (Xbox, PC) - "Interactive Drama" with a wild story. From the same studio and precursor for Heavy Rain, Beyond: Two Souls, and Detroit: Become Human.
These ate just a couple off the top of my head that I haven't already seen posted here.