First things first: Your kid has to pay rent. Seem harsh? Remember that the goal is to get Mikey or Jenny back on his or her feet and out the door, and that means accepting adult responsibilities. The dorm wasn't free. The apartment wasn't free. Your house shouldn't be, either.
A child's reaction may be anger and surprise. This is where they grew up, and they may have been hoping for a place to lick their wounds and be a child again. But while you can provide that support emotionally, financially is another matter.
You don't have to charge the market rate for rent -- after all, your kid is probably at home due to a financial slump. It's more of a symbolic gesture that lets your kid keep some self-respect and keeps you from feeling taken advantage of.