Well I saw youtube videos even yesterday. But now I see this message...
your browser does not currently recognize any of the video formats available
Can anyone tell me how can I fix this in Ubuntu 14.04?
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You should install a package called "ubuntu-restricted-extras" with this command in a terminal:
sudo apt-get install ubuntu-restricted-extras
Actually, installer offers to do it for you but you may have not checked it up. This package brings various parts that may be illegal in some countries, so they are kept out of installation images. This contains archievers, encryption software and media codecs.
as @Barafu said, you haven't given much information as to your setup.
i would suggest using the Google Chrome browser, and trying to enable HTML5 video playback in YouTube (rather than using Flash video)
try checking https://www.youtube.com/html5 to see if it is enabled in your current browser