Suppose I wanted to create a "game" running on Etherium's global computer; perhaps one that allowed people to own and breed virtual cats. I might want a random component in my "breed" behavior.

Imagine I want to create a smart contract where tasks are created by customers and assigned randomly to "turks" who submit completed tasks and are paid (if the task is accepted). A random number might be one useful part of the task assignment process.

ANY program that would random numbers is a potential candidate.