The other night I set up a Google Doc for a class activity and it was pretty successful. What I set up was a doc as accessible with link with full editing rights. This allowed everyone with a link to have full access even if they did not have a Google account. For our activity we had four groups answering questions about their respective libraries simultaneously. It was kind of neat watching this document get co-constructed with four students adding content at the same time. At the end every student had the completed document as take away.
How is this useful to you. Lets say you are working on a project in small groups. Students could use Google Docs as the medium to create and share. You could use a table like I did with each group adding content in a specific section of the table. Or you could have a Doc with questions with each group answering one of them. It will probably work best if each group has its own section.
If you are a 2nd / 3rd grade class this could be a way for you to give students access to note taking / research without having a Google Account. You could create a folder with a document for each student that is accessible with link with full editing rights. In this situation, I would set permissions on the folder not each individual document. When a student goes to the url they see a folder with all the student names. They would just need to find the one with their name. Again, your students would not need a Google account for this and the document would remain in your Google Drive.
Along a related theme you can do the same thing with forms in Google Drive. You could create a form - think survey or quiz - and all the collected data could go in a spreadsheet. And while we are at it, you could follow the same setup as Docs, and have students create a presentation in small groups. Not only could they include text and images, but also YouTube videos. Lets not also forget Google Drive also has a drawing program that can be utilized in its own right or through Docs.
Lastly, you can utilize netbooks or iPads for the above activities. With older students they could just go directly to there account on either device. With students without that access create a link they can access like I described above. I would create a short url with tinyurl or goo.gl for easy access.
If you give these ideas a try, share in the comments about how it went.