As a shopper on the Internet, the thought of sending a credit card number into cyberspace makes many people baulk; indeed some people simply refuse to do it. However, using your credit card on the Internet is no less secure than using it over the phone or fax.
Indeed technically, sending it over the Internet is often more secure due to the encryption technologies now in place to code your number. The real danger of course lies in dealing with shonks at the other end who could load up your card with all sorts of bogus transactions.
This is where you need to use your judgement, though my general advice on this is not give your credit card number to anyone - be it over the Internet, by phone or even in person - unless you're confident you're dealing with someone reputable.
While credit card details sent over the Internet are generally secure, electronic mail is not as secure and I'd advise against sending any confidential information this way. With a secure website, your details will be deleted as soon as the payment is processed. E-mail doesn't have this high level of technology, and there's more room for human error or carelessness. Most websites offer a fax facility for payment as well.
Credit card companies don't advertise this widely, but in the unlikely event of someone getting your card number and using it, the same rules apply as if you lost it in the street. The important thing here is to report it immediately so the card can be cancelled and a new one issued. If you are still concerned, you can authorize your to pay the merchant by transferring funds from your account to theirs. The Commonwealth and St George banks are among those who provide this facility.
Sending money anywhere to buy from direct mail has its risks, so my advice is, only buy from a site you trust and that has a track record.