Companies are rubbish at this
Banks can be quite good.
Had a similar thing happen to me, £160 to sainsburys, £180 to new look, caught it within the hour (the person using it was changing my verified by visa password, so i got the e-mails), got in touch with the bank to stop the card, then both companies. Pointed out that they could:
a) send the goods, then have the money reclaimed off them by my bank
or
b) not send them, refund the money, or just hold the goods then cancel the order when the money got reclaimed

Took them so long to respond, that i doubt they actually did anything (used the online system, found out about this late at night, and had already spent quite some time on hold with the bank, so didnt fancy their customer care lines).

Another couple password changes happened (VbV is exactly as secure as not using it, the only piece of info you need to change the password you don't need to do a normal transaction is the issue number, which is "1" on 90% of cards.), but this was after the card had been stopped.

I then ended up waiting for ages for the new card due to my own incompetence (forgot my account address was set to my term time one, which I'm not due back at for another month (this happened late July)).

The bank (Alliance and Leicester) were great (aside from the first CS person i spoke to, who misunderstood and thought I was trying to cancel my own orders, not one someone else had made), the cash was back in my account as soon as the transactions cleared (they cant refund until it shows up on the statement), I just couldn't get to it due to the aforementioned own stupidity.
( Tedium Alduce me to interlow myself., Sat 4 Sep 2010, 15:09, Reply)