Most games (and probably all RPGs) have this pattern somewhere within them: attempt a course whose fulfillment is uncertain, make a decision, try your best, see how it goes. Game uncertainty tends to involve luck (look how common dice are!) and game decisions tend to involve meaningful choices (whether it's sneak vs fight or one NPC's life vs another's), but trying your best in RPGs seems pretty hit and miss to me -- sometimes it matters, but a lot of the time it doesn't.
Maybe "pick a move from a list and roll" is a natural way to free up brain space for another sort of performance -- performing your character for the other players, and contributing to a vivid and engaging imagined fiction. Sometimes, that's exactly what I want -- to enjoy playing pretend, and to let a simple formal system push things forward without taxing me.
Other times, though, not so much.
When I'm playing some badass operator who fulfills a tactical niche on his team, and we're going on a mission, then simply enjoying the flavor of the experience is not the first thing that occurs to me. My first impulse is, instead, to apply myself to the mission -- to think of the right questions to ask, to invent new solutions to problems, to react quickly to surprises, to act out convincing maneuvers or deceptions, etc. This helps me feel like it's me there on the mission, and that every moment of play is important. And it feels awesome when I earn success, rather than just my character earning success.
Unfortunately, I haven't run into a lot of support for this in RPG land. I've yet to find the RPG equivalent of Cranium, the board game which challenges you spell words backward quickly or mine your real-world knowledge for facts or depict something recognizable with pencil or clay. The best support I've found out there to reward my performance is The Right GM, often one guided by reality-simulation principles, or fair-challenge principles.
What other options are out there? What RPGs, or subsystems of RPGs, satisfying your cravings to have your best efforts rewarded?