Win 7, 64, Home, Adobe Flash Player ActiveX 11.8.800.175, Adobe Flash Player Plugin 11.8.800.168, Firefox 24.0 (IE 10, Maxthon 3)
This may have started when I updated Adobe Flash Player 11 ActiveX to 11.8.800.175 on 9/27. All youtube videos in all browsers play video fine but no audio. Some websites with embedded flash play audio, some do not -- none with embedded youtube flash play audio. No problems with the Volume Mixer. Have run FireFox in Safe Mode and same problem. Computer audio outside browsers works fine. VLC, Windows Media Player all work fine. Problem is only in the browsers. I have K-Lite pack installed. Everything has been working with no problems.
Well I have solved the problem and do I feel pretty stupid. Although I must say that this is easy to miss. It appears that the latest Flash update leaves the Flash player with the volume slider turned all the way down. It is unmuted but you don't see the volume slider unless you hover over the mute icon. Once you turn it up it is set for the Flash player for all videos. It never ceases to amaze me the decisions that software developers make.
Honestly I had the same problem, I tried to update my flash player and nothing happened. So I finally went to shut down my computer and it said restart & update, I clicked that, kept my laptop plugged in and it restarted. Now it works just fine! Hope this helps someone!