This was the problem faced by Sanaklp, one of my friend. He was trying to install some apps via apt-get. during the installation he was warned about for no space in root partition. Somehow the system was working fine even after all this. But once he rebooted his system, he couldnt see any sub-menu under "Applications" menu. At the moment i reached there and he asked me to resolve the problem.
I thought that some configuration associated with the menu must be wrong and I was right. I just deleted the config file at /home/
$ rm /home/<username>/.config/menus/applications.menu
What happens after you delete this file is the system assumes your menu to be same as the default. Whenever you change the menu (Right click and "Edit Menus"), the system will again generate the file which you deleted earlier.
Relogin and your system must be fine now.