How are you planning to offer this? You can install a ftp daemon on the server and then add virtual FTP users where you can back up data to. A daemon like pure-ftpd will allow you to setup virtual FTP users and also quotas. Or you could create a normal user on a linux server, and use filesystem quotas, but I wouldn't recommend this unless this box is solely a backup server and you're locking it up tight.
Is this for you or clients? I'd strongly suggest http://www.bqbackup.com/ if you were looking to use a 3rd party to do this.
First create FTP account then use rsync to transfer your backup files to FTP server. rsync is the safest and easiest method to transfer files between servers. You should prepare a cron job as per preferred time to transfer backup files automatically.
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When I read this first, for some reason I thought he was going to start a backup company.
If you're going to simply backup users website files, then BestServerSupport's response is fair enough. You will probably want to setup a reverse rsync on the target node or other method of ensuring that if your source node is compromised, an intruder cannot tamper with the backed up data as well.