At the very least, I would hold them until the next one comes in, to make sure your previous payment is shown on it. I had an issue once where I made a payment on a store card bill, but the following bill didn't show it, and I was charged for missing the previous month's payment. Because I had the previous bill with a receipt for the payment stapled to it, I was able to have the payment applied to my account, and got a refund of both the overdue charge and the extra interest I had been charged.
It's also useful to have a bill or two to use as proof of address when applying for loans/mobile phone contracts etc.