How Important Is Intuition?

We all have intuitive feelings about things. Sometimes these intuitions can be right, and sometimes they can be wrong. In some cases we need to overrule these feelings with logic, but in some cases it seems that our intuition adds value to our lives.

How can we determine which is which? How important is intuition?

Related questions: How can we improve our intuition? How does our intuition change as we age?