If you want to disable root from being able to login via ssh edit /etc/ssh/sshd_config and find PermitRootLogin.  Change the value to no.

# Authentication:
LoginGraceTime 120
PermitRootLogin no
StrictModes yes

If you wish to disable all password logins which requires uses to use public keys instead in /etc/ssh/sshd_config and find PasswordAuthentication.  Change the value to no.

PasswordAuthentication yes

If you wish to diable password logins for only some users add the following to your /etc/ssh/sshd_config file

Match User user1, user2, user3    PasswordAuthentication no