Ah, Planescape: Torment. The best computer role-playing game of all time. It features a very intricate, interesting plot that will make you shed a tear by the end of the game.
You control a character called The Nameless One who uncovers his past as the game progresses. You are in Sigil, city of doors, in the Planescape universe (an AD&D setting), and you will meet bizarre creatures and strange people in a journey to find out what your destiny is.
Nothing is conventional in this game. Abilities are not raised just by your stats, but rather by your actions. Wisdom and Intelligence are far more important than Strenght and Dexterity if you want to unravel the mystery of your past. There is no armor, but tattoos that grant special powers; your party members seem to have met your before, and your best buddy is a floating skull.
To say more is to spoil the best role playing experience one can have on the computer. Play this game, and *know* you will enjoy it immensely.
Just a warning, though: this game is not for people with short attention spans who get bored at the first line of text. There is a lot of reading and lots of dialogue, all important to understand the plot and fulfill The Nameless One's destiny.