Ok, here is what happened. I tried to install the newest version of Flash on Firefox (34.0.05). On the download page it shows correct system information:
Windows 64-bit , English, Firefox
I close both browser and Skype and proceed installation. After that I launched Firefox and Flash Player crashed multiple times when I tried to play videos on YouTube. On Chrome and IE I saw video but it didn't have sound.
I used uninstaller and followed instructions on Adobe's Flash Player Troubleshoot page to remove Flash Player completely and rebooted. Same thing happened again when I tried to install the newest version. So I removed it and installed older version (15) and it seems to work just fine, though Firefox is trying to block it all the time.
Any idea what could cause this?