Is there an API to get the list of all Google groups a user is part of (of course, with his/her permission) and vice versa (given a Google group, get all users part of that group).
The Google Apps Provisioning API lets you retrieve the current memberships for a Google Apps user as well as list all members of a Google Apps Google Group. However, there is no way to do this for consumer (@gmail.com) Google Accounts and regular (@googlegroups.com) Google Groups.