How do I set VLC media player as default video player?

Go to System Settings → System info → Default Applications, and set it there. It works in Ubuntu 11.10 (Oneiric Ocelot).

In Ubuntu 13.04 (Raring Ringtail) and later, it's found in System Settings → Details → Default Applications.

Rightclick any video file, choose properties. Choose Open With and there you can select VLC and the option set as default (bottom right).

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14.04 and 16.04 also has this option:

Ubuntu 13.10, 14.04

Click on the gear icon in the top right corner then select the option About this computer. From that set Vlc media player as default application for opening videos.