The ActiveX version will only work in Internet Explorer. If you're using a different browser, then you need to go to http://get.adobe.com/flashplayer/ and download it for that particular browser. You may also need Shockwave For Director too. Here's the link for that: http://get.adobe.com/shockwave/
You don't mention which operating system you're using either.
Incidentally, if you have Firefox installed, download this Add-on: https://addons.mozilla.org/en-US/firefox/addon/download-youtube/?src=userprofile
Then when you go to any video on Youtube, you'll see a button underneath it called "Download". Click that to download it to your own machine. This might work even if the video doesn't actually play.
If you haven't got Firefox, you can download it from here: http://www.mozilla.org/en-US/firefox/fx/