Below, Pat argues that players in a rpg have a greater influence on an overall rpg experience than the system the players use. As a lawyer and social scientist, I often think about the interaction of people and binding rules that govern behavior. I'm not going to argue with Pat that the skills, knowledge, and dispositions of the players sitting around a table aren't very important, because I think they are - I think Pat's post well demonstrates this. But I do believe that the system is very important as well.
Let's start with an example to draw out some ways in which system may matter: Pat and I played in a Mutants and Masterminds game together for about a year and a half. This game has very robust rules to support combat on a D&D style battle map (M&M is D20, after all). But the game has very few mechanics to support social interaction or the effects of personal characteristics (like a nasty scare or fame) in the game. Our GM had a great handle on the rules and could instantly process the interactions of different rules in new situations. He ran a clean combat, and he didn't spend too long on non-combat scenes. When he did spend time on non-combat scenes, it was pretty free form, and I was rarely left satisfied that my character was dealt with fairly or adequately.
I would argue that this situation demonstrates the importance of system. Without mechanics that support or facilitate certain types of gameplay, this gameplay either didn't happen or happened in a free form and ultimately unsatisfying way. With a different GM who cared and thought more about social scenes and personal characteristics, I might have had a more satisfying experience. But even a game with players and a GM who really want to focus on social scenes and personal characteristics would benefit from mechanical support for these types of scenes.
Indeed, don't we often play particular games because we like the rules and the types of interactions they frame? Yes, unless we're so in love with the game's setting that it just doesn't matter. don't we play Settlers of Catan because we like the rules about expansion and building? Yes, unless we love bargaining with our friends and don't get other opportunities to do it. Isn't engaging with the rules in strategic and creative ways a large part of what makes rpgs fun? Yes, unless you're completely focused on story, story, story. And even then, the rules can help turn story creation into a game.
The players are very important in rpgs, but much of the gaming experience results from the interaction between players and system. When the system does not have robust rules to govern a type of situation, little attention or free form play in that type of situation results. With a bevy of strong players, the free form play can be fun. But the experience isn't always fun or fair, and it starts moving deeper into that grey area that's between gaming and making up stories.