1) Portal 1/2
Valve-style storytelling at it's finest. Even if you don't prefer sci-fi this is a must play. Linear.
2) Metro: Last Light (Although boredgunner has already recommended this I though two recommendations might help you see how good this is. )
Post-Apocalyptic FPS with tons(TONS) of conversation that could be easily missed. But if you're really interested in a story & some fine(FINE) atmosphere, this is the games. If you decide to play this, play Metro 2033 first. Although it doesn't have the amount of conversations in Last Light, it's still beats most of the games out there.
S.T.A.L.K.E.R Fan Club