I'm using the default installation of `openssh-server` for my Ubuntu 14.04 server. I can connect through the console as root like normal, with my username and password. When I try to SSH with the same username/password, however, I repeatedly get Access Denied errors. `/var/log/auth.log` reports `Failed password for root from <ip address> port <port> ssh2`, but I'm entering the correct password.

Why can't I connect to the server via SSH, even though the username and password ARE correct?