From a recent interview with Jonathan Ive of Apple:

Something I found very interesting was Ive’s response to the question,”When you are coming up with product ideas such as the iPod, do you try to solve a problem?”

His reply:

There are different approaches – sometimes things can irritate you so you become aware of a problem, which is a very pragmatic approach and the least challenging.

What is more difficult is when you are intrigued by an opportunity. That, I think, really exercises the skills of a designer. It’s not a problem you’re aware of, nobody has articulated a need. But you start asking questions, what if we do this, combine it with that, would that be useful? This creates opportunities that could replace entire categories of device, rather than tactically responding to an individual problem. That’s the real challenge, and that’s what is exciting.

Now this is fascinating for me, because we are taught to always ask the question, “What’s the problem that this is trying to solve“, when designing or developing something new. Ive says revolutionary products come when you ask “What can we do with this?“.