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?
Hackers will bang away with root user trying to brute force their way in. If you are going to allow root logins, you should definitely install Fail2Ban, or something similar to protect against brute force attacks. Also use a very hard to guess password without the use of common words.