As many as are synced via iCloud. I currently can switch between iPhone, iPad, Mac (multiples), Macbooks (multiples), and Apple TV and also Apple Watch. I also have them paired with my gaming PC and some gaming consoles but those don't automatically switch. I have to go into a Bluetooth menu and connect them but that's quick and no different from most Bluetooth headsets. The in-ecosystem stuff is the killer piece for me.
