ProjectM is a standalone visualization app that plays the WinAmp MilkDrop visualizations. It's engine is what powers the visualizations on XMBC, Clementine and others.

It can be installed stand-alone and will play visualizations for whatever is pumping out of your speakers (technical: it taps into pulseaudio to "hear" the audio).
This way you can use your favorite media player even if it hasn't got visualizations.
To get it, search for ProjectM pulseaudio
on Ubuntu Software Center or install straight from the terminal with:
sudo apt-get install projectm-pulseaudio
Then launch it from unity by typing ProjectM
on unity search.
The Ubuntu wiki page on ProjectM has some keyboard shortcuts for controlling ProjectM, including the f
key to toggle the all-important full-screen mode.