You could indeed see if rsync would do the trick. You can take incremental backups with it if you like (see something like this
), but in any case I do not recommend taking backups to NTFS volumes nor FAT. NTFS is not a native filesystem to Linux and while support for it is nowadays commonly included into distributions, I don't recommend using it if it's not a must. FAT32 (not to mention the older ones) can't hold big files and it doesn't have a clue about permissions the way Linux-native filesystems (for example ext3) have, and therefore you're going to run into problems at some point. When taking backups you generally want to copy them in "archive" mode, preserving permissions and so on, and FAT just doesn't do that. I'm not sure about NTFS, never cared to look at it that much. Put short, use the same filesystem for your backup media that you use for your production server, and you're probably good. If you don't think your production server filesystem is as "good" as your backup media filesystem, perhaps consider changing it as well.
Even with rsync (alone) you can't probably acieve a situation where you can just point and click to have a system restored completely while it's still running. For recovering some files it's ok, but if your system is in a condition where you'll need to perform a 100% restore from a backup media, you probably are going to put it off line for a moment. Maybe you should have a look at RAID (disk mirroring) as well?