Merv, I'm not sure if the European cards have RFID in them any more frequently than cards over here do. European cards do, however, use a "chip and pin" system rather than a "swipe and sign" system. In case you haven't noticed, you can use any "signature" you want with your credit card...a smiley face, X, line...whatever. With chip and pin cards, you must enter a pin to complete a transaction, making them much more secure. For Americans traveling abroad this can be a hassle. In Copenhagen, for instance, I couldn't get any of my cards to work at the kiosks to buy bus and train tickets since none of my cards are of the chip and pin variety.
You can minimize the hassle of stolen card information by carrying multiple cards. When I travel I keep several cards in my wallet, which I keep with me, and several more in my hotel. If one of my cards is compromised or my wallet is lost/stolen, I just pull out the backups, cancel the lost/stolen cards, and deal with the paperwork when I get home. If you want even more assurance that you'll always have a card that works, get cards that use different networks (Visa, MC, AMEX) and from different banks.
If you have multiple cards and bank accounts, check out Mint.com. It aggregates information from all your accounts (checking, savings, brokerage, credit cards, mortgage...) and makes it easy to keep track of charges, balances, etc. Mint has good apps for iPhone and iPad that allow you to keep track of finances wherever you are. I use cards from several different banks and this allows me to keep track of them all from a single website or app.