In old Kingdom Rush. No matter whether you are or aren't logged in when you run it, it asks you to log in anyway, but the frame where you're supposed to do it fails when you don't allow Flash to store data on your computer. It sort of defies the purpose of online save, plus there's no such problem in KR: Frontiers -- when you're already logged-in, the game recognizes it and doesn't request another authentication.
Yes, it does. Update: You don't actually need to allow the game to use any space, but it still needs a Flash cookie on the disk. If you change the Flash local storage settings from "Never allow' to 'Ask', everything is fine. Still, KR: Frontiers works fine without Flash cookies.