I heard from some folks that it's wise to collect a receipt after you pay with a card. The reason they propose is that the merchant can theoretically charge your card again after you leave, and a receipt will help you to prove that you did not make this second payment.
To me, it sounds like complete nonsense, but I would like to make sure that it's safe not to take receipts with me after paying with a card (regardless of whether it's debit or credit, confirmed with a pin code or a signature).
Keeping a receipt does allow you to verify that the expected amount was charged/debited it also can help when you need to return an item.
Regarding double charging, the credit card companies look for that. If the same card is used at the same vendor for the same exact amount in a short period of time the credit card company will flag the transaction. They assume either a mistake was made, or fraud is being attempted. The most likely result is that the transaction is denied.
A dishonest vendor can write down the card number, expiration date and CVV number. Then after you leave make up a new transaction for any amount they want. You of course wouldn't have a paper receipt for this fraudulent transaction. The key is reviewing your transaction history every few days: looking for unexpected amounts, locations, or number of transactions.
I've seen many people sign a restaurant credit card receipt and walk away. Easy enough for the wait staff to add a tip and total. I doubt this is a high risk area compared to others, but in general, why not take the receipt for verification, or in the case of a good that can be returned, the receipt might be needed.
It surely doesn't HURT to keep a receipt. I tend to pile up receipts in my desk drawer, never look at them, and then every few months throw them all out.
If a vendor writes a receipt by hand or if the cash register is not tied in to the credit card system, keeping a receipt could give you evidence against mistakes or fraud. Like if the vendor gives you a receipt for $10 and then sends a transaction to the credit card company for $20, you could use the receipt as evidence of the problem.
But if the vendor is trying to really cheat you, the most likely thing for him to do is run the legitimate transaction through, and then some time later run a fake transaction. So say today you go to vendor X, buy something for $20, and he bills your credit card $20. Then a few days later he bills you another $100 even though you never came back to the store. Sure, you have a receipt for $20. But you don't have a receipt for the $100 because you never authorized that transaction. Your receipt proves nothing -- presumably you're not disputing the $20. If you complain to the bank or go to the police or whatever, saying, "Hey look, I don't have a receipt for the $100" doesn't prove anything. How do they know you didn't just throw it away? It's difficult to prove that you never had such a receipt.
It is probably safe to throw away the receipt. Without a system to process and store receipts, they are of little use.
With regards to personal finances I'm guilty of preaching without practicing 100% of the time, but here are some arguments for keeping receipts.
To reconcile your statement to receipts before paying the credit card bill - people make mistakes all the time. I bet if you have an average volume of transactions, you will find at least one mistake in 12 months.
To establish baseline spending and calculate a realistic budget. So many people will draft a budget by 'estimating' where their money goes. When it comes to this chore, I think people are about as honest with themselves as exercise and counting calories. Receipts are facts.
To abide by record keeping requirements for warranty, business, IRS, etc...
Personally, the only thing I've caught so far is Bank of America charging me interest when I pay my bill in full every month!
In this answer, I won't elaborate on the possibilities of fraud (or pure human error), because something can always go wrong. I will, however, explain why I think you should always keep receipts.
When the (monthly or so) time comes to pay your credit card bill, your credit card company sends you a list of transactions. That list has two primary purposes, both of which I would consider equally important:
While for the former item, a receipt is not necessary (though it certainly does not hurt showing the receipt along with the bill to provide further proof that the payment was indeed connected to that bill), the latter point does require you to store the receipts so you can check, item-by-item, whether each of the sums is correct (and matched with a receipt at all). So, unless you can actually memorize all the credit card transactions you did throughout the past one or two months, the receipts are the most convenient way of keeping that information until the bill arrives.
Yes, your credit card company probably has some safeguards in place to reveal fraud, which might kick in in time (the criteria are mostly heuristical, it seems, with credit cards or legitimate transactions here getting blocked every now and then simply because some travelling of the actual owner was misinterpreted as theft). However, it is your money, it is your responsibility to discover any issues with the bill, just as you would check the monthly transaction list from your bank account line by line. Ultimately, that is why you sign the vendor copy of the receipt when buying something offline; if you discover an issue in your list of transactions, you have to notify your credit card company that you dispute one of the charges, and then the charging vendor has to show that they have your signature for the respective transaction.
So, to summarize: Do keep your receipts, use them to check the list of transactions before paying your credit card bill.
EDIT: The receipt often cannot be replaced with the bill from the vendor. The bill is useful for seeing how the sum charged by the respective vendor was created, but in turn, such bills often do not contain any payment information, or (when payment was concluded before the bill was printed, as sometimes happens in pre-paid scenarios such as hotel booking) nondescript remarks such as "- PAYMENT RECEIVED -", without any further indication of which one of your credit cards, debit cards, bank accounts, stored value cards, or cash was used.
