Quite often we go on websites (other than trademe) and purchase say hotel accommodation, airline tickets etc, both in NZ and overseas. We understand traffic to and from these sites are encrypted, and generally regarded as safe.
For our coming trip we have recently booked hotels. WE emailed one about their special deal, and we received an email from one of them advising us to give our credit card details. We told them we are not comfortable with this, and they told us to fax the credit card details. We faxed them the number, and gave the expiry date via email. That was all they needed to hold the booking for us (similar to taking an "imprint" of your credit card when you check in). Another hotel we booked via their website, and we gave the credit card details there, and the correct sum was deducted.
Another time we went to book air tickets for local flight in China using a local site, they claim they were having lots of problems with overseas credit cards, and they demand a long list of verifications such as photo copy of front and back of credit cards, and of passport etcs. We promptly switch to another website, and successfully did our booking without all the "authentification" of our cerdit card.
We know of friends and family who refuse to use credit card on the web, or do online banking. We have been doing online banking, and purchases on the web, for quite a while, and, touch wood, have had very little problems. HOWEVER, we do wonder how SAFE is it, to hand over your cerdit card details (number and expiry, and sometimes signature), either by phone, fax, email, filled form etc?