Ingredients those with sensitive skin should look for?

Thank you so much for the input.  This has helped me quite a bit, especially coming to the realization that the fragrances could be the main culprit.  My previous way of thinking was that the non-scented soaps were more for people looking to avoid having contrasting soap and aftershave scents or those who get headaches from strong scented products (like my wife).  This thought process was further perpetuated by the fact that most scented soaps do not provide me with any type irritation/itching.  My belief, which in essence is still true, was that it was the amount of a certain ingredient (previously discounting the fragrance) that caused the reaction, especially since most (all?) soaps do not list the percentages of each ingredient.

I had this problem last year because I am very sensitive and allergic to many substances. Until one day, I decided to take some lessons about it. I started looking for esthetician schools in my town. When I finally found one, I discovered that their program was about advanced aesthetics, and it had a chapter about Ingredient and Product Selection.