aramis erak
Legend
Most of the Fate games released before Fate Core, in fact.It is rare, but games that have players taking active hand in campaign design do exist - The Dresden Files RPG, (Fate-based, for those who care) has an entire minigame for campaign design with the players, for example.
John Wick's games (excepting Blood & Honor and it's parent, Houses of the Blooded) put that definitional authority into the "Game of 20 Questions" by having the players define significant elements in character generation. This aspect was downplayed a bit but still present in the FFG rework.
All games from Burning Wheel HQ explicitly make it so.
All but one of the over a dozen AWE/PBTA games I've read put the majority of setting into the hands of the players, almost nothing at start in the GM's hands. Even the peripheral-to-that-ecosystem of games moderately strong GM game, Sentinel Comics, leaves a lot to players.
Hero System has strongly suggested players involvement in campaign building past the level of character definition, with a goal to producing a campaign document which defines the allowed ranges for powers, skills, disadvantages, and attributes. I first encountered this mode in Champions 4th ed.
John Wick's Houses of the Blooded and Blood & Honor both reserve to the GM two powers: to introduce fully defined characters, and to award Style/Honor points. Any player on any risk (the term for a dice resolution sequence - it's actually comparable to a whole round of most other games) can introduce and/or define and/or modify any character, item, or situation. Anyone can introduce a new character at any time via a Risk. Anyone can alter an existing character at any time when they're in the scope of the Risk's initial action. In other words, if they're in scene, they're targets.