Memorable Programming Assignments?

Albert Schueller asks: "This fall I'll teach introductory programming for the third time. The class is generally populated by students from a wide range of backgrounds and interests-liberal arts and science types. While we use C++, the language isn't really the issue. Rather, the goal is to introduce basic programming ideas like loops, logic, modular programming etc. What are some of your favorite programming assignments that would be appropriate for students at this level?"