1. Email List

Email Lists are great for sending out announcements or communicating in a clear way to the entire organization. It is often set up with an alias as the sender and non-group owners are only allowed to respond to that sender. I often see this used to distribute newsletters or to let everyone know about important events or happenings.

2. Web Forum (discussion board)

In a web forum, group members use the Google Groups user interface to interact with one another. It allows for collaboration and discussion amongst the group members. A popular use case for this type of group is discussion of assignments if you are working together on projects.

3. Q&A Forum

Very similar to the web forum, the Q+A Forum is designed to allow for discussion around specific questions. Much like an internal version of Quora, this style of group promotes question asking and encourages your users to answer posted questions to which they know the answer.

4. Collaborative inbox

This is the most popular type of group at many organizations. Anyone can email the group and start or reply to threads. Think of this as a regular gmail account, but everyone has access to it. A Collaborative Inbox is primarily used for lighter discussion amongst the whole organization, kind of like a chatroom.