Briefly describe your idea
Public reports that users can use to show information based on the groups they are in, not predefined groups.
Why is this important, when it would it be used
This will simply report creation because the report can be defined once and be used by many different users to show the information that is relevant to that user.
If you were designing the solution, how would you do it?
Add a 'My Groups' special filter critera that will apply based on the user who is viewing the report.