How can I get my webcam to work with Ubuntu 14.04?

UPDATE: Actually, I just found that you need to manually add your user to the audio and video groups. The easiest way is to launch the "users and groups" app and go to manage groups

Original answer:There seems to be an issue with the permissions on /dev/video*.

They are owned by root with no read/write permissions for regular users. My quick-and-dirty hack was a simple:

sudo chmod 777 /dev/video*