So, this is more or less a well known bug that Skype on Linux doesn't support too much webcams. Well, in this tutorial, we will solve this bug.
First of all, you will need to go to your home directory. In my case, it would be /home/alex/. Now we will create file (by right clicking in nautilus and selecting Create document -> empty file, or if you prefer command line, then touch skype.sh). Then we need to right click on the created skype.sh, select Properties and click on the Permissions tab. There we need to check "Allow executing file as program" box (again, if you want to do it with command line, use chmod 740 skype.sh).
Now we need to edit it with your favorite text editor (mine is Gedit, gedit skype.sh) and paste in the following lines:
#! /bin/bash
LD_PRELOAD=/usr/lib/libv4l/v4l1compat.so skype
and save it. Now we've got what we wanted! Double click the skype.sh, skype starts and your webcam should work!
You can also update your shortcuts to Skype (if any) to use the command /home/your_username/skype.sh instead of skype. In my case, this would be /home/alex/skype.sh
Hope all works ok!
Of course this should work on any Linux based OS, not just Ubuntu. Thanks goes to Nobbit for finding this useful fix.

Source of the fix:
http://ubuntuforums.org/showpost.php?p=6115686