As I think of ways I have used Google Apps in my teaching, with peers and students, several things come to mind. I will begin with using it with MY peers, the teachers in which I work with.
I am currently in graduate school, working on a Master's in Administration. In doing so, I have to complete A LOT of papers, data analysis sheets, conduct surveys, and so on. One way Google Apps has helped me to do this is sharing documents through Google Docs. I can send surveys in a Google Form and the responses come to me already organized in a table. This allows for easy analysis and discussion. I have also used Google Docs to share and collect data with my PLC. I created a document and shared with the team that allows them to just add the data into the spreadsheet. The document automatically calculates our averages for student, question, and grade level. When shared with the assistant principal, she took it to the county to be shared with the county.
I haven't used Google Apps with my students this school year but did use it two years ago with my high achieving students. When we completed our poetry unit, they did all of their poems and assignments through Google Docs for me to analyze and give suggestions to and then they uploaded their work to their own website. The website was branched from my classroom site so they could share their work with family members all over the world.
All of this is "THE GOOD"! I LOVE Google Apps and how easy they are to use. I wish I had more computers in my classroom to assist all of my students so that pencil and paper would not be the main tool in seeing their work.