I was removing my son's band-aid, and in so doing I was hurting him. Half way through, I had a brilliant idea. I went to the kitchen, soaked a bit of paper towel in vegetable oil and applied the vegetable oil where the band-aid was separating from the skin as I peeled the band-aid. Result: the band-aid separated with much less pain, as the vegetable oil dissolved the adhesive.
Obviously, it's not a good idea if there is an open wound. And one has to clean off the vegetable oil, perhaps with a bit of soap.
I got the idea from the fact that one can remove self-adhesive stickers with vegetable oil. (I used to use WD-40 and then discovered that vegetable oil works at least almost as well.) A later web search showed that other people discovered both uses for vegetable oil (e.g., see here).
Anyway, I'm posting this here in the interests of decreasing the amount of minor evils in the world.