If, in your home or office, a computer is functioning as a file server, it's certainly worth considering whether you could use a network volume (AFP, SMB, or otherwise) as a backup destination.
In general, if you have control over the server yourself, I recommend adding a separate physical hard drive and installing client-server backup software. Otherwise, your backups will be commingled with other files, making it difficult to store them off-site and potentially creating a security risk.
If you do not personally have control over the server (i.e., if it's a shared company server), be circumspect about using it for backups. You could easily use up more space than you should, and you risk incurring the wrath of your IT manager. Even if she's willing to give you your own capacious partition on a server hard disk, you'll have much less flexibility and control over your data than if you backed it up to local media.