We're working to resolve this issue.
Sorry for any inconvenience caused.. we really want this to work for you.

We have just applied a fix for the security code problem, where upon hitting process my order, the security code field was highlighted as invalid.
Please let us know if it works and allows you further process the payment.
Thanks!

For some users, their bank's fraud monitoring systems have flagged their payment attempts as suspected fraud, probably due to the fact that GOG.com is a new company and based in europe.
Please contact your bank and check this.

Put all the games you want into our shopping cart and then process the cart in one transaction =)

Have you got any kind of javascript blocker eg. NOSCRIPT? I recommend turn it off for a test, to see if you can process the transaction to the end.
Here's a short explanation:
In our payment screen, when you have to click process, there's a inlay (I'll check the terminology and edit) which appears, the screen as if darkens to show only the white box in the middle, which then should connect to your bank's 3D secure site, so some kind of flavour of either Verify by Visa or Mastercard Securecode.
By having NOSCRIPT or similar switched on, your bank's special 3D Secure page's javascripts are disabled and this stops you being able to process the transaction further. Then we get a response from the payment system and we show that error message.
I hope that explanation helps somone =)

The latest updates in the payments system should fix your problems, please try again. If you will have any problems paying for your order now, contact our support.

Leonsito - please write to the support team about the issues with processing payments. They can help you more personally as we shouldn't discuss those problems on the public forum.
Thanks