Who's That Knocking At My Door?

I was looking at my "security logs" the other day, noticed that every few days someone tries to to log into my computer as "root" from the internet (via SSH), tries to guess the root account password, gets shot down and moves on. It looks like it's coming from different internet addresses each time. I'm not sure if it's someone just screwing around (or multiple people), or if it's one or more malware programs randomly sniffing around the internet for unlocked doors.

I don't have many internet-type services running on my machine; other than mail and a web server, which are both blocked from outside use by my firewall, the only one is the SSH server. That is accessible from the outside, and I want to leave it open, but I think I'm going to lock it down a little tighter: no root access, no access using only passwords. Luckily, I have that new book that tells me how to do exactly that...

Didn't go out last night, by the way, just stayed home with the computer and the leftover bruschetta pizza.