Some years ago after using Amazon USA there was a small amount deducted monthly from my partner's credit card from a concern with a just a jumble of letters as a company name. At that time we were not too diligent at checking credit card statements and as the amount was only a few dollars we didn't notice it.
We were alerted to the fraud by the credit card company who phoned one Saturday to enquire if we had used the card for a transacation of $10,000 with this "xyz company inc". Obviously we said no and that's when this whole scam came to light. They had been removing $4.55 from the account for several months, I suppose to find out if we were "statement checkers" and then do "the big one".
All credit to the credit card company for bringing this to our attention. They obviously didn't pay out the $10,000 and we had all the $4.55 payments returned after the fraud investigations had been completed.
This happened in 1996. Since then we have both been checking out statements as soon as they arrived but there has been no further problem. For my own Internet credit card transactions, of which there have been many, I have had no problems at all.
As a point of interest, that purchase from Amazon got lost in transit. Six months later it eventually arived having been literally round the world as for some reason, although most of the address was correct, they had put Papua New Guinea as the country. So, in the six months of being lost it had been from country to country trying to match the reaminder of the address.
Note there was a reason for using Amazon USA rather than UK. It was an American book and the UK company couldn't supply.