Some do, some don't. I have exchanged plenty of things with no receipt and got store credit.
Same here at Target. If you happen to return items which weren't on your registry, they will have it act as a regular return and take your info down. At Target, you can only return up to $75 per year (without receipts) for store credit.
I'm not sure if they check the date of adding items to registry, but if you receive an item without a receipt, add it to your registry and then just take it back to the store. I don't know if this is a no-no and I frankly don't give a shiit, but wish I had tried it myself.