Adobe has released the stable version of Flash Player 9 for GNU/Linux.
If you are interested in the fixes for this release, check out their release notes.

Adobe has released the Flash 9 beta for GNU/Linux. I have been using it for a few minutes and it is quite stable so far.. although one should take care to always remember that it is unstable software.

You have the option of downloading the plugin or a standalone player and you will need to manually copy the plugin to your plugins directory.