How do you deal with hypersensitive people?

[populistmom]

You know the type of people who get upset at the slightest anything resembling a criticism. Or even when you simply point out a difference, all their defenses go up and they lash out somewhat (not physically, but verbally or give you the cold shoulder). It's the kind of situation that I know isn't really me so much, but the less I feed into it and more healthy and uncodependant I am about it all, they worse it gets. Ever find yourself appologizing to make someone else feel better when you did nothing wrong? (I used to, but don't so much now.) And if it's a person that in one way or another, you would never be able to avoid in your life completely? What would you do?