I had the same problem with SuSE 9.3 on a 32bit platform, allthough some sites worked, but the most didn't (e.g. nasa.org).
The problem is that there are two flashplayers installed, the Macromedia one and the Open Source GPLFlash one. What I did was uninstalling both and manually installing the version (rpm) from
http://www.macromedia.com/shockwave/...ShockwaveFlash
Maybe only uninstalling the GPLFlash or the Macromedia Flashplayer will also work.
I think SuSE made a mistake to include the not yet mature open source GPLFlash.
Cheers,
J