Did you install the package called
ubuntu-restricted-extras? You can do this in the Software Center or, if you prefer the to use the command-line, then by running
sudo apt-get update followed by
sudo apt-get install ubuntu-restricted-extras.
If you have
ubuntu-restricted-extras, then verify that a Flash plugin is actually installed by checking for the
flashplugin-installer packages. If neither is installed, install one of them. If you're running the 64-bit version of Ubuntu, installing
adobe-flashplugin is preferable. (But don't have them both installed at the same time.)
If you're running the 64-bit version of Ubuntu and you find that you have
flashplugin-installer installed and the problem continues, then try removing it and replacing it with
If none of the above works, check to see if you're using the HTML5 beta on YouTube! by going to http://youtube.com/html5. Theoretically, and eventually, this should perform uniformly better on Ubuntu. But right now, it might not work well. So if it's turned off, you can try it and see if it works better. If it's turned on, try turning it off and seeing what happens.
If you have trouble doing any of the above, please post a comment here. If you do the above but it doesn't work, please edit your question to indicate that it didn't, and also to include the output of this command (which you should run in the Terminal):
dpkg -l | egrep 'flash|gnash|swf|spark'