I'm using Opera 10.10 and when I go to YouTube (for example) it is asking me to click the grey circle icon "to activate or download the plugin".
You might not be having all the plugins... To install all the opera plugins go to http://www.opera.com/docs/plugins/ and install all the required plugins...
Click the grey circle icon to see what plugins are missing and download and install them. On YouTube and other similar websites, you will need to have installed Adobe Flash Player. If you still have issues, I suggest you download and install Opera 26.0 from the official web page.