I have regifted before, only if its something nice and new and I think someone else would enjoy it. However, I generally add it as a filler gift, meaning I have already gotten them the main gift, but I'll add this strong smelling Bath and Body lotion, because we can't have fragrance's in our home. My son gets migraines from strong perfumy smells. But I usually am just adding it to another already existing gift. If I get something from Harry and David I don't particulary like I will bring it to the family gathering and put it with the food to share with everyone, not give it as a gift.
As far as teachers. If you didn't regift your home would be over run with mugs, and candles and lotions. My mother was a teacher, and there are only so many "Worlds greatest teacher" items a person can get. Knowing that from when I was a kid and my mom got all that stuff, I always buy gift cards for the teachers and try to get my kids to find out something they like. My daughters 5th grade teacher was a Male who loved "Monster products", so we got him a gift card and a 4 pack of Monster. She came home and said he had gotten 12 4 packs of Monster. But at least it was something he liked.
I think its a zing if a person regifts and makes it obvious, or doesn't bother to take the previous tag off. That is hurtful. Hopefully it was a mistake to foget the tag and not intentional.