The biggest thing I've wanted to do was to define a data object that can host Dependency Properties that can then easily participate in data binding. The specific design case isn't the strongest currently, but it's a pattern that I've used consistently in WPF applications to great effect. As it stands, I'm approximating it through post-construction assignment.
Having dug into it more than I had when I originally posted this comment, I'm not entirely sure the current data binding support handles the cases that I was attempting to pursue anyway, but in the long run this would be useful.
Clarification, I was attempting to subclass DependencyObject, not FrameworkElement. Also, making OnPropertyChanged "internal protected virtual" would open up a lot of the event handling and abstraction I was also hoping to accomplish with using DependencyObject.