If you follow the indie game scene, you've probably already heard of Christine Love's Digital: A Love Story, but I had never gotten around to playing it until recently. It is essentially an interactive novel, but while most interactive text stories are told merely with text and hyperlinks or user commands, Christine Love does a creative thing and tells her story through the GUI of the protagonist's computer, and it really adds to the immersion.
On top of that, while it is an interactive story, the interactive components draw the player in without challenging or overwhelming him, and it does this while maintaining linearity and building a strong relationship between the player and one of the other characters. I think this is an amazing feat; in games you usually have interactive components that merely provides the player with challenges while telling a linear story, or you have interactive components that have the player determine the outcome of the story. The problem with the first is that you have a game that is only an interactive story in a very loose sense, and the problem with the second is that it is difficult to create a strong protagonist with motivations and behavior separate from the player, which limits the type of story you can tell. Christine Love somehow has created a protagonist that, even though you control him, has personality and motivations unique from the player. Yet, when I played the game, I felt as though I was one with the protagonist: his motivations became my motivations, his outrage was my outrage. It might not sound like much, but I think that's amazing.
Essentially, Digital: A Love Story it everything that I want my games to be, even if they are in a different format. It's really good, so give it a play.