I was having this problem too for months and today I discovered that the problem was with my Firefox profile. Here's what you need to do:
1) Open up "Run" and enter: %APPDATA%\Mozilla\Extensions
2) Create a new folder named Plugins in the Extensions folder
3) Now open up C:\Windows\System32\Macromed\Flash
4) Copy & paste NPSWF32.dll and flashplayer.xpt into the Plugins folder
5) Restart Firefox. Adobe Flash Player 9 (or greater) should work fine now.