How would you design a server that has to process a fair number of good number of requests a second. What if you didn’t know how many requests you’d be getting? What if requests had different priorities? (I always think of the Apache design for this question)
Design an elevator control system. Don’t forget buttons on every floor and supporting multiple elevators. (What objects/methods/properties/how components communicate)
Design a chess game (what objects? what methods? which data where? how will it work?)
Design a deck of cards class (object/methods/data)
How would you design the infrastructure front half of a very large web ecommerce site? what if it was very personalized? (how sessions are handled? where and what you can cache? how to load-balance?)