How to discover what users NEED and not what they WANT?

I have been thinking a lot about my favorite quote from Henry Ford:

If I asked people what they wanted, they would have said 'Faster Horses'. -Henry Ford

The trouble I have been having is that I know how to make something usable, but I am an innovator at heart, I have to be trying something new.

So what is the way to discover what users NEED and not what they just WANT?

If I do a user test the way I do now, I get their reactions, wants, and desires, which are rather predictable 9 times out of 10. But what I am having trouble with is digging out their needs.