Portal, Penumbra, Antichamber, Quantum Conundrum, Mirror's Edge, off the top of my head. (Mirror's Edge does have some shooting, but it's mostly platforming, and IIRC the expansion pack removes combat entirely.) Portal alone touched off a revolution in first-person puzzlers, and Amnesia/Penumbra did something similar with atmospheric horror.

Ever heard of Gone Home? Definitely worth a shot if you're into nuanced stories.

Proteus is a FPsomething; certainly not a shooter game. Almost barely a game, more of an experience.