I have really enjoyed the story games of Ben Robbins. Robbins is probably best known for Microscope, where the players construct a timeline by telling events in a non-linear fashion. They are light RPGs with a focus on characters and story telling. Most games have no stats or even randomizers (beyond your fellow players). They are easy to get into and so light on rules that one easily may think that it isn't much to them, when they are constructed in a very deliberate way.

I just found out that Robbins has made a free version of his game Follow a couple of years ago. Follow is a game where the player characters go to perform a sort of quest together. It is a good opportunity to try a modern story game for those that are curious.