First of all, let’s define “valuable” and determine which of these items (gift cards, coupons and receipts) fall into that category. The answer is, it depends.
Gift cards are valuable if you are actually going to use them. Some stores will buy back gift cards (at less than the value of the card). There are also online sites that will buy back cards. Some of these are Card Pool, Raise, and Gift Card Rescue.
If you are like me, gift cards are hidden in an obscure pocket in your wallet. I constantly forget that I have them, and so I never use them. A solution for this is to move all your gift cards to the front of your wallet with all your credit cards so you will see them each time you go to pay for something at a store.