Shame is, well, not all that fun to feel. Research indicates that when we feel shame, we globally de-value our entire sense of self. It is basically as if our physiology is telling us that (in our heads and hearts) we are a rather worthless person.
Guilt on the other hand, also obviously sucks, but it isn't quite as bad. Research indicates that when we feel guilt, we are devaluing our specific behavior or behaviors. We don't see ourselves as awful people as we do when feeling shame. Instead we see ourselves as good people who did bad specific behaviors.
(See research on shame and guilt differences by June Tangney of George Mason University).
Anyway, it is clearly a good thing not to feel shame. No one wakes up thinking, "gee, my day would really rock if I could just get a good old dose of shame in today." No one, ever, has thought that.
Research headed by Montana State University professor Matthew Vess suggests that you can greatly reduce the shame you feel by one simple thing: being yourself. Ok, so maybe that isn't as easy as it sounds. But when you live an authentic life, and are true to your values, you are less likely to feel shame. This is opposed to living a life where you do and think what you believe others want you to do, or live your life pressured into doing things.