Sorry for bumping an old thread, but I came across a program called Druuva InSync recently which looks like it works in the same way DropBox does. Other than the initial price (non-educational is $35 per computer) there are no monthly fees and you host it yourself so you have total control over it and your data.
inSync is more like laptop backup, and works for remote users as well. Good software for on-premise backups though.
Address changed. Actually the new website location is - Druva inSync