David Cage's Indigo Prophecy (known as Fahrenheit outside of North America) is an adventure game for the PC, PS2 and Xbox. I played the PS2 version, but the other ones are very similar.
The game is all about story, with the gameplay elements consisting of some arcade-type simon-says action sequences with the dual analog joysticks and some simple puzzles. The game also uses a fairly unique "mental health" meter than can go up and down based upon the things you discover and the dialog choices you make.
The creators call the game "elastic" in that you can slightly change some of the game paths, but only to a small degree--hence, elastic. You are still bound to follow the main story arc, but you hear different dialog and find some other clues depending on your choices.
There are also several different endings, which I discovered after reading an FAQ on the game...turns out I got the "best" one if you can call it that. The story does fall pretty flat at the end, and Cage admits it in his post mortem on Gamasutra.
I did enjoy this game for the most part. The climbing sections (especially climbing down) I found overly difficult and frustrating compared to everything else and there are a few stealth sections that were interesting, just sometimes the difficulty level was uneven. Overall, a good experience. I give it an 8/10.