The GM can create genre aspects, which are campaign-wide, that help define and enforce some common elements. Examples would be Comet Monsters Are Everywhere! for a game where a comet from space empowered random citizens, or Mutant Prejudice for a game where powers come from a genetic mutation that stigmatizes supers born with it.
Just like aspects, stunts can also be tied to a campaign, a particular story arc, or a location, not just a character. In Four Color FAE, such genre stunts can be introduced that break the game rules to enforce a particular convention of superhero games.
Genre stunts are also a way to introduce risky or powerful optional rules. They can provide rules for all characters with a given power fact, such as super-speed, that the GM feels is important enough to articulate but not unbalancing enough to require each PC to have.