Get a monitoring service/server
Additional things I do on UNIX servers:
Lock down user accounts - Even though this is in the Securing Windows list, I gave it special mention here. In the old days, most UNIX software was designed to be used from or in conjunction with a shell account. That mentality has held over to today's software in its default state. If you run an FTP or mail service, and that user only needs to access FTP or mail, there's no reason to give them shell access. Keep that in mind when performing your lockdown - no shell access unless necessary!
Kill X - You don't need a GUI on a server. It's wasteful. Get rid of it.
Compile services yourself - I generally compile all services myself (such as apache, qmail, djbdns). The benefit here is twofold: one, you completely customize the software to your preferences; and two, since you set the software up to your specifications, you'll have a much easier time indentifying and combatting problems. No packages, no binaries, only source. Note: I consider skeleton source port systems (such as those that Gentoo or the BSDs use) to be okay.
Install chrootkit [chkrootkit.org] - Run it regularly, and send the output to someone that will read and act upon the reports.
Install tripwire [sourceforge.net] or aide [sourceforge.net] - Run it regularly, and send the output to someone that will read and act upon the reports.
Get a package update notification service - This is critical. With so many open source software apps, things change daily. I know that RedHat has a service, Mandrake has a service, and there's a bunch of others. I'm biased, and mainly use FreeBSD, so I use FreshPorts [freshports.org].
Install nmap [insecure.org] - Run it against your entire network on a regular basis and send the output to someone that will read and act upon the reports. It will tell you immediately if any backdoor is currently running on a server.
Personal/Political Rant (flamesuit on):
Don't use BIND, sendmail, or a GUI (web-based or otherwise) control panel - These are the top offenders of UNIX security and good practices.