The problem goes further than the cards themselves though, I think the big problem with them is that you have to give companies all of the details needed to make a charge when you buy things online, and those details are stored. Other comments here are right, the main way to deal with this is single use card numbers that can be revoked individually.
I think a good way would be to implement something similar to what OAuth does. When you want to make a payment to Amazon for example, you tell your bank who you are and after authenticating you, they would provide a token to Amazon who can store that to use for purchases. If at some point in the future Amazon were 'hacked', the bank could revoke charging authorization for all tokens given to Amazon, immediately protecting all of their customers.
You also get a failed transaction report, some people can have 4-5 goes before giving up on their purchase. Sometimes to countries somewhere abroad the customer gets a form to fill in to apply for having this extra check on their account (because there is no 3D secure in the country where they have their card registered or it is not customary to use it).
It would be nice to use 3D secure as an extra feature, and, as a retailer, set it on a case by case basis, e.g. to an order that is for somewhere overseas or over a certain value.
In the UK a fraudulent order is a fraudulent order, as a retailer you are on your own dealing with it. Putting someone's card address in Google Street View and seeing how big their house is often turns out to be a good way of deciding whether to 'ship' or not.
Address verification is a 'soft fail' if you want it to be. It will compare the address by numbers, so someone entering 'Flat 2' in the primary address line will fail the system if the address is actually 'Flat 2, 34 Church Street' as '34' is expected for the match.
There is no system guaranteed to work, except Paypal, that you pay for in fees.
These matters aside, the system of swipe only in the US just gives most people in the UK scary feelings.
Having lived in the UK for 3 years, I'm not sure anyone's "house size" over there is a good indicator for, well, pretty much anything ;D
The implementation I can live with. That fact that its opt-in is entirely fatal though. Criminals just need to find a website without it. So the only person inconvenienced by it is me.
(1) It authenticates features of your browser (like user-agent, IP address) to score the transaction. These are somewhat hard for an attacker to duplicate.
(2) With some UK banks, it is combined with a hardware one-time password generator to form a reasonably robust two-factor authentication.
Now there are certainly problems, such as it appearing in a frame, and not appearing as a subdomain of your bank, and those should be fixed.
http://www.cl.cam.ac.uk/~rja14/Papers/fc10vbvsecurecode.pdf
EMV has it's problems. I've worked with a few researchers who have targeted the security of it in several ways and found some quite serious issues, so I'm quite aware of the security implications. However in terms of practical criminal use, having the challenge and response mechanism with the card is a significant improvement over the static data of a magstripe.
That said, an interesting piece of British law is the fact that a signature forgery is never the responsibility of the victim. This means that if someone fraudulently signs for a payment, you are not responsible for the charges at all, whereas if someone watches you enter your PIN, or you tell it to someone and they subsequently use it to make payments, this is your responsibility. The grey area for a while was that the companies behind EMV said it was 'uncrackable' (never a good idea) and refused to take responsibility of charges that some users claimed had been made without their PINs being revealed by them. Anderson, and the Cambridge security researchers demonstrated a proof of concept a few years ago that showed how it could be used without knowing disclosure of the PIN, and since then card companies and banks have been a little more receptive to taking on the responsibility.