I have had a company (children's book of the month club) triple charge me once and had to contact them about it. They were great, fixed the issue and sent me a voucher for a free book.
On the flip side, I work in e-commerce and hear this complaint often enough. 99.99% of time time, when I hear someone say they were double or triple charged, the issue is this:
They submitted their credit card information for the order and either the billing name/address or the CID number on the credit card was entered incorrectly. The credit card system rejects the authorization and the customer corrects the information and resubmits the order. Depending on how many times the credit card info is resubmitted, it can create multiple authorization holds. Normally, there will be the one authorization hold for the full amount and then a number of $.01 holds, which correspond to the amount of times the credit card info was pushed. The problem comes in when the order ships quicker than the holds drop. When you have one authorization hold and then the order ships, the pending hold gets converted into a charge but when you have multiple holds going on and the order ships, the actual charge may not replace the hold that is for the amount of the order. Then, you are looking at your credit card/bank account and you see a hold for the order amount and a charge for the order amount and assume you have been double charged. If one of them is listed as pending, the bank/cc company will remove the hold and the length of time that takes depends on their policy.