I've used Mambo/Joomla for several sites I've developed, the latest being for the non-profit trade group Automatic Fire Alarm Assocation of New England.
http://www.afaa-ne.org
The framework is ideal, because it allows community participation. I echo the sentiments of many when I say that better access control is needed, but I understand that is a priority moving forward.
For non-profits, a common thread is that most need to attract, service and retain members, and promote events, both which allow the organization to continue. I'd love to see a component (are we still calling it that?) geared towards this segment that can manage these types of things. I use AKReservations (kudos AK), as this does much of what we need as far as events go. But a comprehensive event management component would be very valuable.