If you don’t see your webcam video on Skype, in Options » Video Settings menu, the solution is to install Video for Linux 1, as you probably only have V4L2 libraries.

This is for users who encounter problems with Skype on 64bit Debian/Ubuntu. If this is you, then you should install libv4l in 32bit flavor.

apt-get install --reinstall libv4l-0:i386

Now the nasty thing is you have to run Skype like this every time:

LD_PRELOAD=/usr/lib/i386-linux-gnu/libv4l/v4l1compat.so skype

But at least it solves the problem.