- Amber Diceless Roleplaying: A game that shattered many of the rules of older style RPGs--no dice, character auctions, incredibly freeform rules. This was the first RPG I encountered that strongly emphasized doing what was dramatically appropriate, not what was realistic or advantageous to your character (it may not have been the first to do so, but it was the first that I saw). With the right group, this is a great game.
- FUDGE: Steffan O'Sullivan's game did a number of things that I think shaped the future Indie movement. First, he relied very heavily on the internet to get feedback and promote the game. Second, he built a game to emphasize telling stories, not crunchy combat. And Fudge incorporates a lot of verbal elements; things aren't just about numbers. At the very least, Fudge exercised a huge influence over Fate which is a detailed variation of Fudge, as is The Shadow of Yesterday in some ways.
- Over the Edge: A brilliant and very weird game. This was the first game I ever saw that had no defined stats or skills; you created your own for your character. This alone had a huge influence on games like RISUS, the PDQ system, and arguably Fate's Aspects (although I'm speculating on that last one). It also featured a simple and elegant dice mechanic, character design that gave you tons of hooks to roleplay with, and a very cool and bizarre setting.
I could be wrong about the influence these three games had, but it seems to me that many of the key features of Indie games appeared here.