I guess this depends a lot on what sort of questions you are talking about. If it's life and love and "soft" things like that, intuition is probably better than any decision based on "data", what ever that would be. On the other hand, if you just have an intuition that you should set the price at $1,000 rather than $99, it might be worth at least exploring your own thinking.
There is nothing wrong with having strong intuition and then looking for data to back it up with. It's a sound psychological foundation -- read Antonio Damasio's book Descartes' Error for a fascinating exploration of this idea. However, intuition can be wrong. "Following your gut" is sometimes praised as if gut feelings are some super natural source of knowledge. They are not. They should be guidelines, but you should still question them and be open to new realizations. Besides from conversations with people of different views, 5 whys (http://en.wikipedia.org/wiki/5_Whys) might be a useful tool for this.