At one time, though, premature babies were displayed as if they were zoo animals. A physician named Budin, one of the inventors of the incubator, displayed premature babies at the Berlin Exposition of 1896 and in subsequent exhibitions. A student of his, Dr. Martin Couney, also displayed premature neonates at exhibitions, including as late as the 1939 New York World's Fair. It sounds pretty trashy to use babies in such a way, but before we judge them too harshly, realize that Budin did studies showing that survival of premies weighing less than 2000 grams was improved if their rectal temperature was kept normal, a significant advance for the time, and Couney, although a showman, is said to have cared for 80,000 premature infants during a 40 year career.
Frankly, I think exhibits of premature neonates would still be popular at fairs, since it's not uncommon for hospital workers and visitors to want to see them. This is especially true if the babies are a set of multiples, like triplets or quadruplets, making them minor celebrities. It's also a problem if one of the parents is a hospital employee. I remember when an OB resident had her baby; there were OB residents making a steady stream into and out of the NICU.
Earlier in my career I wasn't sure how to handle requests from friends in the hospital who wanted to see the babies. I'd let them see them sometimes. I even took my mother around our NICU once, to show her the kids I worked with. (Not a medical person herself, she couldn't wait to get out of there.) But now I have an easier time refusing their requests. For one thing, I can claim that HIPAA doesn't allow it, although I'm not sure if that is really true, and for another thing, I'm just grumpier than I used to be and don't care if people are miffed at me for not letting them in. Also, I truly do worry about infections. The NICU is no place for extraneous people, people who might be incubating a cold and not know it.
I've never really asked parents how they feel about strangers looking at their kids. I suppose different people would have different thoughts. Most parents are proud to show off their baby, but if their kid is struggling for life on a ventilator, making him an exhibit isn't high on their list of priorities. The exception is if you ask the parents if you can show their baby to students as a teaching case. For example, a baby might have an omphalocoele, a defect where part of the abdominal contents are outside the baby instead of inside him, or some other unusual finding that students won't get to see often. If the parents aren't around, I simply show the baby to the students, but if the parents are there, it's only right to ask for their permission. They rarely refuse it.