I want root user to be able to login via ssh key authentication. How can I get that done? I tried changing the ssh config file and adding PermitRootLogin without-password but that didn't work. I also tried reload sshd. I'm using centos 6.
Assuming you have done everything right (as per comments above), and it still doesn't work - the problem (and I hit it regularly) relates to SELinux rules.
You can check that this is the case by [ temporarily ? ] disabling SELinux by "echo 0 > /selinux/enforcing" and see if things start working.
Apparently the solution would be to log in to the box and run "restorecon -R -v /root/.ssh" (I confess to not doing it this way, I just used corepolicyutils and made a ssh.pe file which I copy and load on each system which has this problem).