Q:

Good challenges/tasks/exercises for learning or improving object oriented programming (OOP) skills

What is a good challenge to improve your skills in object oriented programming?
The idea behind this poll is to provide an idea of which exercises are useful for learning OOP.
The challenge should be as language agnostic as possible, requiring either little or no use of specific libraries, or only the most common of libraries. Try to include only one challenge per answer, so that a vote will correspond to the merits of that challenge alone. Would also be nice if a level of skill required was indicated, and also the rationale behind why it is a useful exercise.
Solutions to the challenges could then be posted as answers to a "How to..." question and linked to from here.
For example:

Challenge - implement a last-in-first-out stack
Skill level - beginner
Rationale - gives experience of how to reference objects

A:

Building Skills in Object-Oriented Design is a free book that might be of use. 
[EDIT: The original book appears to have bitrotted (404s for all formats) but the Internet Archive has versions as HTML, PDF and MOBI]
The description is as follows:
"The intent of this book is to help the beginning designer by giving them a sequence of interesting and moderately complex exercises in OO design. This book can also help managers develop a level of comfort with the process of OO software development. The applications we will build are a step above trivial, and will require some careful thought and design. Further, because the applications are largely recreational in nature, they are interesting and engaging. This book allows the reader to explore the processes and artifacts of OO design before project deadlines make good design seem impossible."

A:

Write a challenging program from scratch. Try to get some people (around five, that should be doable) to use it. Respond to their change requests.
Adapt your program's design. Start small, then watch it grow. Manage this growth. This is hard. You will also have to fix bugs and maintain the thing over time, which for me was a very valuable lesson.

A:

Challenge: Write a wrapper for your web site/service API of choice in your language of choice, that doesn't already exist (ex. a ZenDesk API wrapper written in C#).  Release the wrapper as open source for others to use.
Skill Level: Beginner to Intermediate
Rationale: To learn how to extrapolate a 3rd party web service API into a meaningful set of objects/classes, making the reuse of that API easier in your chosen language.

