Update: Opera 9.50 seems to solve this problem. Check your version and update if needed.
After a serious vulnerability had been discovered in Acrobat Reader for PDF, one of the leading products from Adobe now becoming a standard, which affected all browsers now the online video format they are also trying to introduce as a standard doesn't work with some browsers. You can check that Flash plugin for Linux (it seems that also affects Windows) doesn't play FLV video with Opera (you can also find cases with Firefox or Konqueror). You can find many reports of many users with this problem, I also had my fight with it. Finally, Gentoo Bugzilla gave me the answer:
sed -ie "s/netscape/flashsux/g" /opt/netscape/plugins/libflashplayer.so
Supposing that /opt/netscape/plugins/libflashplayer.so is the location of the plugin, it will be fixed and you'll have a Flash plugin suitable for any browser. But this fix has an issue: it's illegal because it violates Flash EULA), so I can't recommend its use :-).
In the same source is cited a legal solution consisting of locating the plugins in browser plugins directory:
ln -s /opt/netscape/plugins/flashplayer.xpt /opt/opera/lib/opera/plugins/flashplayer.xpt
ln -s /opt/netscape/plugins/libflashplayer.so /opt/opera/lib/opera/plugins/libflashplayer.so
Supposing that /opt/netscape/plugins is the directory where Flash plugin is located and /opt/opera/lib/opera/plugins is the browser's plugins directory.