Drive
Welcome
Drive is pretty awesome and has numerous other uses (you could easily have an entire class just on Drive applications). They introduced Drive (and integrated Docs into it) in 2012 as a competitor to services like Dropbox, iCloud, etc. You get 15Gb of data FREE, and 100Gb is just $2/month. Aside from the huge amount of storage, Drive is also the home of Google's suite of office apps plus a lot of other barely related apps:
Obviously, you can do all sorts of things with this - basically anything that you'd do with Microsoft Office, but with fun perks like detailed revision history, cloud-backed auto-saving, and integration between the apps. Rather than go into how to use each app, we'll just look at a few neat uses for the classroom.
Giving Student Feedback
With Google Drive, you can add comments to students' work. They can see these comments live and even carry on a discussion, turning ignored comments into corrective instruction.
Revision History
You can view the revision history of a document (under File for some reason...), even going back and restoring revisions. This is obviously helpful with changing mistakes made over the course of days or even months, but it's also really useful for when students are working on something collaboratively, allowing the teacher to see just who did what.
Translate
You can translate your document into about 50 different languages, making it a great way to send home letters to parents.
Forms
I almost gave forms its own page, because it's such a big tool. You can create quizzes for students to take in class or on their own time, or surveys, or reading logs. I've used it before at Open House to have parents leave me their contact information.
Apps and Add-Ons
Apps and Add-Ons are great but this page would get ridiculous in length if I talked about them here. Click the link in the navigation pane on the left side of the page or, better yet, just click here to go to my page about Apps and Add-Ons for Google Drive.