I'm looking for software that will auto-backup files from a remote server to a local server ONLY if they have been modified or added. Otherwise they will not do anything. Is there any software available like that?
In addition to the rsync answer I can totally recommend rdiff-backup. It is based on rsync, works across different operating systems and file systems and is absolutely reliable. I use it myself to back up different computers to different others, across local networks, the internet and dial up lines. But the nicest feature (for me, YMMV) is the easy restore of data at any given point back in time. Almost as cool as Mac's timemachine ;-)
I use this:
It sits on an OS X server connected to an Exabyte tape drive, and I have it backing up data from OS X and Windows servers alike... It can be configured to perform backups as you have described...Not cheap or open-source, but I've found it to be reliable..