Even if you think your password ist strong. This will stop a majority of the brute-force password-guessing attacks. For extra credit, install denyhosts as well. It has stopped a _lot_ of bad guys trying to brute-force my servers.
More important is to routinely rotate strong root passwords. What most people neglect to mention, when denying root access to an SSH server, is that people then login with a second account, (you still need ssh), and then su - to root. So, all you've really done is moved the difficultly in logging onto the server from the root account, to the secondary account+root account. Your security is now based on the strength of that bi-pair of passwords. As others have mentioned, moving logins to RSA keys (very easy) is probably a better approach.
In /etc/ssh/sshd_config, disable root logins:
PermitRootLogin no
Even if you think your password ist strong. This will stop a majority of the brute-force password-guessing attacks. For extra credit, install denyhosts as well. It has stopped a _lot_ of bad guys trying to brute-force my servers.