Is there any desktop utility for OS X that would periodically monitor a (non-osx) server and display a status icon? Something as simple as attempting to visit a URL every 5 minutes and turning red if it does not respond would be enough, although anything more detailed is interesting too.
GeekTool will let you set up a simple icon or show more detailed information, embedded in or floating over your desktop, based on whatever programming you want.
If you can write a script to check the server and return either a binary status or more detailed information, GeekTool is the way to display it.
ServerSiren ($15 with 10 day free trial)
With Server Siren, server downtime is a thing of the past. It runs as a menu bar item, so a quick glance is all it takes to see that everything is A-OK. If a server goes down, Server Siren alerts you immediately so you can fix the problem and get your site up and running again.