I enjoy good storytelling. Storytelling originally attracted me to the original D&D games but then I found that they are mostly played as an exercise in table searching and dice calculations. If I'll ever play role playing games, I'll certainly want to use some sort of "bare bone" system like Risus or Window.
There is also very interesting storytelling card game, called Once Upon A Time, which I played several years ago and purchased during the recent trip to Japan (there is cool small "Yellow Submarine" boardgame shop in Shinjuku).
The idea is that you get several cards with story elements and one card with story ending and you have to tell a fairy tale, incorporating all the story elements (i.e. getting rid of all the cards) and wrapping it up using the words on the "ending" card. Other players can use some simple rules to "interrupt" your story and change it to conform to their cards (i.e. getting rid of their cards). For example, if you play the "Witch" card and say "The witch lived in the Dark forest", the player with "Forest" card in his hand can jump in and continue the story. It's a little more complicated but not much. As with the original D&D, the game is only fun if you play it to create interesting story, not if you play it to win at all costs.
There is also an expansion called "Dark Tales" which brings some nice tragic elements into the mix, so that you can create cool stories like the following (click to see the large version):