I think this must be a new feature; Adobe Flash Player is now prompting me to update when a new version is available. This is great news--Flash Player vulnerabilities offer hackers a relatively easy way to get into machines where users don't even know Flash is running, let alone which version. Because this seems to be a new feature, it is important for people to make sure they have a recent version of the player. As of the time I write this posting, the most recent version for Mac and Windows is 9,0,115,0. To check which version you have installed, go to About Adobe Flash Player. To download a new version go to the Player Download Center.
To set how often Flash checks for updates (I recommend 7 days), go to the Global Notifications Settings panel. There are other settings panels you can adjust from there.
For more info, see About Updating Adobe Flash Player.
NOTE: Many Windows computers will have two installations of Flash--one for Internet Explorer and one for Firefox or other browsers. You may have to open each browser and check the version / run the Flash update.