Well, one day I stumbled on something called OwnCloud.
It is a free piece of software that can be loaded on a server that is running Mac OS, Linux or Windows. There is a .99 client that gets loaded on the iPad/iPod/iPhone/Android. There is also a free client that can be downloaded to your computer, and the service is also web based.
We quickly built an old Mac Mini into a test server, and loaded the software up. We had this working in under an hour, and plan to build a bigger server for use district wide. OwnCloud works exactly as advertised. You create accounts, log in, and you can move things to the server. I have created some shared classroom accounts for teachers, and they can have kids log in to the account and hand in their work. The service works better than Dropbox, and I own the server, which is important when dealing with students who do not have the ability to agree to the terms of service from online entities. Because we own the server, we are able to provide this to our students without a problem.
Check out the OwnCloud web site here - http://owncloud.org