Dropbox and connect it with a service like File Stork to collect files online.
File Stork allows you to collect files in two ways. You can make an individual file request by sending an email to someone. The other way, and the more practical way for teachers, is to create a "stand alone" request which will allow you to post an upload link on your blog or website. Visitors can then use that link to upload a file to your Dropbox where you can view it and download it if you like. File Stork allows you to specify an upload password and allows you to specify which types of files you will allow to be uploaded to your Dropbox. People uploading files to your Dropbox through File Stork do not have access to any of the files in your account.
Applications for Education
File Stork is similar to Dropittome which I implemented on my course blog last fall. Services like File Stork and Dropittome are great for cutting down on inbox overload and quickly accessing the files your students submit to you.