There are two items in the Show menu in the Activity center that deal with this exact issue. To be able to see completed activities and projects, make sure that these items are both selected:
- Completed projects
- Completed activities
These options are user-specific, not global. That means that if one user (even an administrator) changes them, the change will not affect what other users see.
Another way to enable showing completed objects is to use the filters in the Activity center.