Sometimes (on LiveCDs for example) you might want to allow users with no password (passwd -d user) to use GDM.

There are two changes to be done. First, edit /etc/pam.d/system-auth and find the pam_unix.so module for the auth action:

auth            required        pam_unix.so try_first_pass

Add nullok to that module's parameters:

auth            required        pam_unix.so try_first_pass nullok

Second, edit /etc/gdm/custom.conf and add the following line to the [security] section:

PasswordRequired=false

Now either restart GDM or kill your current X session with Ctrl+Alt+BkSpace.