Other than remote login, there's various useful things you can do with ssh, like running a remote command, multiplexing connections to save on server resource, setting up ssh aliases to save you some keystrokes, and so forth.
Recently, when my partner logged on a recently created CentOS server hosted at Digital Ocean, he saw the following messages:
Last failed login: Tue Jul 29 16:27:31 EDT 2014 from stuff2share.net on ssh:notty
Clearly that wasn't us trying to log in. Obviously, there was some malicious user(s) likely trying to enter our server with brute-force attacks. We were under a ssh brute force attack. Such malicious scan is not uncommon these days. It came just a couple days after our new server was up.
I learned a few good ways to prevent this: