The problem

You may encounter an issue where the Adobe Flash Player plugin will flat out refuse to download or install in Safari on Mac OS X, regardless of what you try. Symptoms include:

• The Flash Player plugin download page on the Adobe site fails to download the package. After clicking the Download button, the page goes into the "busy" state but nothing is ever downloaded. The status bar reads something like "X out of Y components/parts downloaded." (or a similar message, I have a non-English Mac OS X)
• Downloading the Flash Player plugin package through other means and installing it works for other browsers, but not for Safari.
• Dragging and dropping files into a new e-mail in Mail displays a grey box with "Plugin missing" (or a similar message, I have a non-English Mac OS X).
• Rebooting the computer does not help.
• Uninstalling Flash Player and reinstalling it does not help.
• Updating Safari does not help.
• Viewing the Safari plugin list page (Help > Installed Plug-ins) hangs, and if you wait long enough, it will display "Slow Script" dialog boxes asking you if you want to stop a long-running script.
• There are no stupidly obvious things wrong like "Not having an internet connection" or "Not having enabled plug-ins in Safari" (thanks, Adobe Support)

Here's a non-comprehensive list of system configurations on which I've encountered this issue and have successfully solved it with the fix below. As always, your mileage may vary, but if this fix works for you, then I'd like to hear about your system configuration so I can add it to the list (shoot me a quick e-mail; see here for my address). I'd also be interested to know if you've tried any troubleshooting measures that aren't mentioned on the list above.

A possible fix

The fact that Mail is also affected by this, and that the Installed Plug-ins page hangs should ring a bell. This suggests that the problem is due to some kind of system-wide plug-in that is shared between various "Internet applications", amongst which are Mail and Safari.

As is indeed the case. It turned out that on my system (Mac OS X 10.5.8), the following file was the culprit:

/Library/Internet Plug-ins/JavaPluginCocoa.bundle

This was a symlink to /System/Library/Frameworks/JavaVM.framework/Versions/A. For a reason that is not yet entirely clear to me, removing this file from the /Library/Internet Plug-ins folder instantly solved the problem (although people have suggested that it might be a permissions problem). After removing that link from the Installed Plug-ins directory (I'd recommend moving it into its sibling directory Installed Plug-ins (disabled), the plug-ins list in Safari loaded up immediately again, and the Flash Player started working perfectly.

This fix is somewhat imperfect in that presumably you'd lose Java functionality in your internet applications, but I can live with that. If you can't, then I'll be glad to hear how you've continued to build on this solution.