Increasingly more modern RPGs are curtailing the "omnipotent power" of the Game Master (GM). More and more games seem to be appearing these days with specific rules telling the GM what he or she can/cannot do. Many games have a resource that GM's have to actively earn and spend to do whatever.
For the most part, I think this is a good thing. Not because it dispels the whole "the GM is a god" thing...which I think is patently ridiculous...but because boundaries can actually create ideas. Sometimes, the blank canvas of the human imagination is so full of possibility it can be easy to become paralyzed (in boardgames, this is called "analysis paralysis"). Having some limits on what you can do and when you can do it filters the number of options a GM has to consider down to a manageable number.
My concern with this new school of game design thought, however, is that its not looking at gamers who are new to the hobby, gamers who may approach an RPG the same way they would any other game. With everyone having checks and balances on each others' power, I'm afraid some games (especially games full of new players) could devolve into who-gets-to-do-what, where even the most altruistic player is struggling to put some kind of order to the general chaos of play, but lacks any real tools/authority to do so.
Old-school GMs get it. They know the truest goal of a role-playing game: everybody should be having fun. Other players care about that, too, but the GM is in a unique position to achieve that goal, by being simultanouesly outside of and around the game. By necessity, this requires the GM to have a certain authority to direct the flow of action, so that everyone is getting a piece of it, and its existence never becomes too stale. This is an unspoken responsibility of a GM, one that they willingly assume the moment they purchase the book, take time out of their days to read the rules, and organize/host the game. The players who don't do any of those things don't have that agreement so upfront in their minds, and so when it comes time to play, they're only thinking of themselves. Not because they're selfish, but because that's what a person does: they sit down to a game, they play it, they have fun.
I think this situation has developed over a thing that's unique in the current tabletop RPG landscape: the hobby is now old enough to have a real divide between generations. The newer generations...let's put the line at the original D20 system, in 2000...don't have the instincts of "make sure everyone's having a good time" hard-wired into themselves, and thus appreciate a game where the GM has the power to make that happen. The older generation, who have been doing this kind of thing for decades now, don't need another RPG where one person is (from their point of view) arbitrarily placed on a pedastal while the others grovel at his or her feet.
So to sum it all up..."power" in a role-playing game is, strictly and exclusively, the power to instill fun in others. Understood and used responsibly, this power not only works flawlessly; it seeps into the very psyche of the wielder. It gets to the point that they don't need to have that power bestowed on them anymore; it's just always there. And so they don't even need the trappings of those games with the older mindsets anymore; in fact, they appreciate the uniqueness and fresh perspective of a game that understands that as well as they do, and thus tries something different, like restricting or disseminating the GM's power.