In a traditional D&D-style perspective on GMing, while character sheets and rulebooks have a lot of authority on the visible or known universe rules and state, the GM's the authority on the unknown universe state. They probably know who's alive, who's dead, and where things are, though they could change their minds if they wanted to, since no one would know. (I guess technically dice have some authority on the unknown universe state, when they're used for random encounters and such.) The GM might add stuff based on player suggestions, but the ball's always in their court, and mostly they're creating an illusion that the setting's all predetermined, that the reality is the model of the world in the GM's mind.
The thing is, the players have a model of the world, too. Even traditional games tend to do some of this implicitly; asking "Is there somewhere I could buy a sword in this town?" is probably more likely to get you a weapon shop than "What shops are in this town?", depending on the GM and how heavily they've pre-specified stuff. And this implicitly gets used in a lot of "say yes" situations, still focused on player actions: if the player says "can I break a chair leg to get a wooden stake?" and you say yes, then you've let the player define several things about the scene (that there's a chair, that it's made of wood, that it's possible to break the leg without a roll, that a broken chair leg is usable as a wooden stake). Some games also use it more directly, such as declarations in Fate (which I guess got sorta nerfed in Fate Core?) or various question-based things in Apocalypse World.
Chuubo's gets into this some, with XP and quest actions. If someone's trying to use a slice of life action, say, they might say "can we have a scene where we're sitting on a bench overlooking the ocean and eating grapes?", which adds different bits of their world model to the game then you'd likely get otherwise. Quests often have specific scene elements that they motivate players to introduce, which has a similar feel; while in some sense they're adding Jenna world model to game more than player world model (if you're using quests from the book), they're open-ended enough that they'll likely add player world state as well, and quite possibly spark them to elaborate their world state in the process.
Dogs in the Vineyard has an interesting take on a different side of the world model. In D&D-style games, the GM is often the authority on character alignment/what the gods think of things. In Dogs in the Vineyard, while rules and moral judgements are a key part of play, the GM isn't in the position of judging, and the state of each PC's soul is up to the player. (Which reminds me a bit of the "death of the GM" thing in LARP-writing, where you can't tell someone they're playing their character wrong despite whatever intentions you had writing the sheet.)
You could imagine a more collaborative, "say yes" perspective to the game canon where stuff that hasn't been determined through play is in an uncertain state that everyone has access to. Some forum roleplays and such do this to an extent. I haven't encountered a tabletop system that goes "all the way" there; Chuubo's seems like it could be pretty close with some rules for players taking turns playing NPCs/antagonists (and a group of players that's all sufficiently confident about describing things). I'd be interested to see how something like that, or a rotating-GM setup, would work in practice.
EDIT: On the last point, I forgot about some of the indie games I have but have never played that are very heavily on the "collaborative storytelling" side of things: Universalis and Microscope. They effectively have everyone as the GM, which is sorta the direction I was going, but I feel like not having PCs would probably be a very different from what I think of as a tabletop RPG. There's also Becoming, which effectively has one PC and ~3 GMs.