It is extremely rare that a secure transaction becomes compromised due to the technology, assuming that the appropriate encryption protocols are implemented, and implemented correctly.
1) Like others mentioned, whenever you are submitting sensitive data over the internet, make sure the URL begins with "HTTPS://", and you see the little padlock icon in the lower right corner of IE (assuming that like 95% of us, you're using IE).
2) Always keep up with the latest security patches for your operating system and browser/email applications.
3) Some of the due diligence relys on the consumer. I have no problem submitting credit card information to Amazon.com, but would never do it with "Billy-Bob's Electronics 'R' Us". It's funny, some people are paranoid about entering CC numbers in Amazon.com, but have no problem handing over their card to the minimum wage 19 year old high school dropout at the local WallyMart. My wife's CC # was stolen just this way.
4) Most credit card info that is stolen off of a server is because the security of the server data and/or box has been compromised. The web site operator has not applied all the latest security patches, has not locked down services/settings appropriately, is storing CC numbers in text files instead of a password-protected and encrypted database. In fact, CC numbers should never even be stored on a web server. They should be stored on a seperate box behind the firewall. Is the database server secure itself? What personal have authorized clearance, IDs, and passwords to physically access the data or the box? Is it in a locked room? Can a janitor grab a backup tape sitting next to the server? I've worked with companies that spend $20,000 on security hardware/software/consulting/development, but leave backup tapes laying all over the place.
So in the end, it is human error and oversight that causes the most breaches in CC transactions, not the technology. Be selective with the e-commerce sites you choose to do CC business with. Reputable ones likes Amazon and PayPal will most likely have invested heavily in putting the appropriate technology in place to guard your sensitive data.