1) “Design and code a system that can accept millions of events in real time and report the number of events for the last 10 minutes (sliding window). The system has to account for performance and concurrency.”
http://www.glassdoor.com/Interview/Design-and-code-a-system-that-can-accept-millions-of-events-in-real-time-and-report-the-number-of-events-for-the-last-10-mi-QTN_187032.htm
2) Design a URL shortner service :
http://www.hiredintech.com/app#the-system-design-process
3) Design a unique id service like youtube
http://kvz.io/blog/2009/06/10/create-short-ids-with-php-like-youtube-or-tinyurl/
4) Design an Elevator System and give the objects involved and their interactions.