In his blog, "Vacation Time is a Great Time to Establish Yourself," Bud Bilanich sites the opportunity presented for a person to get noticed by taking additional duties when co-workers are on vacation. I agree with this sentiment, but the opportunities do not stop there.
There are many more instances where a person can take that step to move beyond their positions current boundaries. Besides co-workers' vacations (or even maternity or disability leave), it can happen when a colleague is overworked or overwhelmed by a new project and needs assistance with duties. Of course, these duties may appeal to you and attempts can be made to take them on permanently. It is a similar thing with the instances a colleague leaves for another company and there is a hole left in the organization.
Looking at the bigger picture, these rare events in your company should not be the only time a person takes on new duties. Every day should be an opportunity for such growth. Pitch a new idea to your manager and explain how you could implement it with only a minimal hit on your daily duties. Or volunteer to manage new work when a new project comes up. And if someone else gets the new project, you could always propose an addition to the project that you could handle.
Careers are living things and they can only grow by the amount you feed it.