Blade Runner - The Game.
When it came out in 1997, Blade Runner the game was somewhat of an oddity. Coming fifteen years after the original film release, the game chose to not even directly follow the plot of the movie it was based on. It featured familiar sets and characters, but followed a new protagonist and new incidents.
But the game was a cult hit. Branching storylines, the ability to set an emotional stand-point for your character and multiple endings made the game unique for the time in that your every action really did have an impact on the path and outcome of the story.
Head over to Godisageek.com to read my Retro Review of the game and find out why you really should play this forgotten gem.