Just Beam It is a free service for quickly sharing files up to 2GB in size. To transfer a file to someone else just drag a file from your desktop to Just Beam It in your browser. After dragging and dropping your file Just Beam It will generate a link to it that you can share with anyone.
I tried Just Beam It last fall. Since then the service has received some useful updates. The two most important updates are support for all modern browsers and support for multiple file uploads. If you upload multiple files, Just Beam It will zip them together on the fly for your convenience.
Applications for Education
If the email service in use at your school can't handle large attachments, Just Beam It could be one way for students to share files with each other and with you. Just Beam It offers a Chrome Web App that you might find useful too.