It seems they haven’t quite worked out all the kinks out of Flash Player 9. My work machine started having an issue where sites couldn’t detect that the player was installed. Instead they would offer a link to Adobe to install the player. Clicking on the link would show a page that indicated that the plugin was installed, but going back to another page that used Flash would still not work.
Pages would fail seemingly randomly. I was just ignoring it, until youtube stopped working.
I googled a bit, and found that all types of people were having this problem. At first I suspected IE7, but people reported the same problem with IE6. After a while, it seemed like the common thread was Flash 9, and I found a post that suggested uninstalling Flash 9 and installing Flash 8.
This worked for me. The steps are easy.

• Get both the Flash 8 archive and the Flash uninstaller
• Close down IE as well as any programs that use IE components (Rhapsody gave me problems, for example)
• Run the uninstaller
• Look inside the Flash 8 archive and find the r34 version of the flash installer. Run it.

These four steps fixed the problem. Not too many sites seem to require Flash 9 yet, so hopefully Adobe will get their act together by the time I really have to upgrade.