It depends on who I'm giving a gift to.
If it's for a shower/wedding then I remove it, as I usually buy something from their registry list.
But if it's for family I usually leave the price tag on, and I even go so far as to put the receipt right in with it so they will have an easy time if they need or want to exchange it, especially with the granddaughters. They are teenagers now so it is hard to know what they would really like/want.