I’m not sure I have a favourite mechanic, as generally I try not to think in those terms. A lot of my games employ a simple two-action per turn format. I think it is important to present players with simple choices that have complex consequences.
My opinion is that the game is its mechanism. Any discussion around this point is just an exercise in theory. When you have a working mechanism you have a game, and when this mechanism is enjoyable, you probably have a good game.
I really focus on the core mechanic and I only start digging into my design if the core mechanic is solid, fun, and provides you with good decision-making opportunities. If this is the case, then I know that adding other things will make this game even better.