To resolve a diamond-shaped inheritance problem. (B and C both inherit from A. What happens to A's attributes in D that itself inherits from B and C?)
A client of your library could see a RedWidget and a FlyingWidget, and might want to combine them into a RedFlyingWidget.
User would have to specify one of the base classes to be virtual when inheriting. But that is not responsibility of a library maker.
OOP flows better with single-implementation inheritance, so that's what I'd use throughout a library.
There are also "upside-down inheritance" trees, as described by Alexandrescu's excellent "Modern C++ Design." They allow clients to pull in more functionality in a form of mix-ins that are called policies.
Programming with policies allows for greater ability to combine functionality, at the expense of syntactical cleanliness. Think STL implementation, for example.