Form+ comes into the picture. Form+ is a third party service that adds features to Google Forms. Probably the best aspect of Form+ is that through it you can create forms that can accept file uploads. Form+ offers pre-made form templates for you to use. You can also create your own form templates through Form+'s drag-and-drop interface.
Randy Rodgers shared a Form+ tutorial on Google+ earlier this month. I encourage you to watch his tutorial to see Form+ in action.
Applications for Education
If you have been looking to expand your use of Google Forms, Form+ might be the tool for you. Using the option to collect files through upload could be a good way to organize students' assignments. Simply create a form for each assignment and post it on your classroom blog to have all of the uploaded files go into a folder. Form+ has an upload form template ready for you to use and re-use as often as you like.