I just started as a web developer for a theatre organization. They had a design firm build them a site and a custom CMS. This situation would be fine if it were 2004, but this thing has just become so unweildy!
They constantly have to update and move content. So - they have a season of shows - and every time a show concludes they have to archive the large amount of content associated with that show and move everything up. The archived show content goes into a "Past Shows" section.
They have a main top nav with two levels of children and a left nav with three levels of children. Right now, everything is done in this propietary CMS. Since it's difficult to code within the CMS, they save a copy of every pages HTML on the server. Whenever they want to edit, they change the HTML file and then paste into the CMS. This company also hosts the site.
Whenever they archive/move files/folders, the CMS changes the link - making tracking difficult indeed. All in all, it seems like just to make simple changes takes 3x longer than it should.
I've worked with custom WordPress themes and I'm assuming for a more complex website Drupal may be an option.