Just finished upgrading from Ubuntu 13.04 to 13.10. Everything works fine. After the installations, I restart to finish the installations. In the log in screen, I put my password and then it goes back to the log in screen.
This issue occurs if you have installed cinnamon desktop environment and related to this bug .You have to uninstall all cinnamon desktop related packages.
Press Ctrl-Alt-F1 to get the terminal from your login screen (Thanks to Ray) or use SSH and run the following commands
sudo apt-get purge cinnamon*
sudo apt-get autoremove
After running above commands i have to reboot my PC to work as normal.
If you have any other solutions please share with us so that it will help some users.