Centos6/RHEL6 don’t have the System > Administration > Login Window menu item. So there is nowhere in the GUI to enable auto-login of a user. If you have a single-user environment and aren’t worried about anyone approaching your console then this is how you enable the auto login.
You need to edit the file at /etc/gdm/custom.conf
su - vi /etc/gdm/custom.conf
You need to edit the daemon section of the file and add or change these:
Then you need to reboot and you’ll be logging in fine.
Credit on this goes to Sudhaker: http://sudhaker.com/23/centos-rhel-6-autologin