No, not that Indy Jones.
Just about everyone has heard of indie films, movies made on small budgets by unknown companies that manage to be a little more daring and avant-garde in their stories. But not many people know about the indie RPG scene. Like those indie filmmakers, indie RPG publishers push the boundaries of what makes a game.
While opinions differ (significantly in some cases, so be careful out there!), my understanding is that "traditional" games focus on representing the world, providing "reality models", much like the physics engine in a video game. They vary widely in how much resolution the system provides. Some of try to stay very close to reality, like GURPS, while most feature some level of "cinematic" or action movie-style realism, like the HERO system or Fuzion. The main advantage of a system like this is that it can be applied to a wide variety of worlds because the rules are generally applicable.
Indie games have rules that emphasize story and character over the world.
FATE and Burning Wheel are both excellent games that focus on characters. Both reward players for making decisions that are "in-character" even if it isn't the most practical or effective decision. While White Wolf is one of the major players in the RPG industry, it was one of the pioneers of this methodology, as characters in their game Vampire: The Masquerade had a Humanity score that would rise and fall based on the things that the character was forced to do to maintain their vampiric existence.
The games that focus on story tend toward telling a certain story with near-endless variation. My Life With Master gives players the roles of minions to a cruel and wicked Master (Suddenly, I'm thinking of running this game with the players being Winged Monkeys and the Master is the Wicked Witch of the West). The players then direct their characters through the process of discovering that not everyone is cruel and eventually overthrowing and escaping from the Master.
Adventures in Oz fits my definition of an indie game. For one, it is very much a one man show (me) with a minimal budget. For another, the game is designed from the ground up to tell Ozzy stories. If I had to define the archetypal Oz story in a sentence, it would be "Exploring Oz with your friends." The exploration aspect is covered in the extensive section on the Land of Oz, along with tips on making your own Ozzy locations to explore. The friendship angle is covered with the Oz Point/Friends List mechanic. Making new friends or helping friends that you already have earn Oz Points, which can then be used to get a favor from a friend on your list.
What's your definition of "indie"? What's you're favorite indie game?