There’s a new version of Flash Player 10 available, designated version 10,0,42,34, which primarily addresses security issues. This update includes x86_32 Linux and even a refresh of the x86_64 version. In the interest of managing expectations, the new x86_64 version is not significantly different from the previous x86_64 version. It is different in that it contains the relevant security fixes and perhaps a few other low-risk fixes.
Check the sidebar (“Adobe Flash Player For Linux”) for download locations.
This is the new current version of Flash Player 10, which is not to be confused with the 10.1 beta which was recently released and of which there is presently no 64-bit version. Sometimes I think I need to draw a picture to keep all these versions straight (but where to find software that can enable such creativity?).