Someone referred to this short guide on one of the lists for how to install the newly released Flash Player 9.0 (final version) on openSUSE. Please do not follow the instructions it gives as this could result in your browser seeing two versions of the Flash plugin. In addition, don't download the RPM that Adobe provide as it installs to the wrong location. Someone reported that it worked for them but what I suspect happened is that it left the openSUSE supplied flash-player package in place and they were seeing the old version (the Adobe supplied package is, unhelpfully, called flash-plugin).

So, what should you do? Well, there's an updated flash-player package available in the Mozilla Build Service repo. You can either add the repo to YaST or Smart and update or download the package and install manually.

[My post on the opensuse list with some more details]