After upgrading to Ubuntu 14.04 (Trusty Tahr), my wife found that her webcam (integrated into a Dell monitor) was no longer available in Skype and other applications. The microphone was available, so the USB connection to the monitor appeared functional. The problem turned out to be that she was not in the video group, which is required in order to access webcams. The following command resolved this:
sudo adduser user video
(replace user with your own username)
After this you will have to log out and back in and then you should have access to your webcam.
I’m not sure if this also applies for a new install, so if anyone can confirm/deny then that would be great.