Dropbox is a free, web-based service for storing files and syncing them between different computers. You can install Dropbox on your home computer, and when you save files there (just like saving them in a folder in your regular documents files) they are automatically accessible anywhere you have web access. This is GREAT for those who use multiple computers, because you can install it on all your computers, and every time you save the file it updates the version online. No more worrying about making sure the latest version is the one you are dealing with! Yay!
Although students wouldn't be able to install this on the school's computer desktop, they can access a dropbox account via the web (with their user name and password), so it seems an elegant alternative to the sometimes cumbersome process of emailing files back and forth.
As a bonus, if you are working on a group project, Dropbox allows you to create public folders that you can share with friends. So members of your group/team could all access and work on the same file from different computers, at different times.