When using a credit card in Europe, I've been asked whether I wanted it rung up as dollars or euros. Is there an additional cost to using one over the other?
ABSOLUTELY -- called dynamic conversion and should be avoided. The business will give you a poor exchange rate AND your credit card company will still charge you the 3% currency conversion even if presented in dollars. That assumes your credit card company is charging that fee. Most do and a few do not. Avoid it, avoid it, avoid it.
Just to make what Frank said more explicit: Tell them you want the charge rung up in euros, not dollars.
So....the best way would be to pay in cash? So as not to carry a lot of cash around, use the ATM's?
It makes no difference whether you pay in cash or use a credit card. You will receive nearly the same exchange rate. We prefer to do 99% cash since, for us, we view it as more convenient. We have both no fee debit and credit cards so that is the cheapest way to go. Some prefer to charger big items and cash for smaller items. On most trips we will only charge a couple items, generally towards the end of the trip when we are managing our cash flow so that we return with a hundred Euro or so in our pocket for the next trip. PS You might find the similar discussion on "How much cash to...." useful.
ring up in euros
Just to add that the same advice holds true regardless of whether the foreign currency is euros, pounds, korunas, forints, zlotys, etc. ALWAYS ask to be billed in the local currency. Otherwise the individual merchant is going to determine the exchange rate, and it won't be to your benefit.
Frank and others here have, with typical Rick Steves' Helpline understatement, given the right advice. Let me see if I can clarify it a little - Don't dOn't doN't don'T DON'T DON'T let them charge you in dollars. Don't. Always put it through in the local currency. Always.
You are seeing a rarity on this site. Complete unity of advice on at least one question. Seldom seem if ever before.
If you want unity, ask if you should use Traveler's Checks. :) Everyone said it well, I tend to use credit cards for major purchases from big businesses (airplane tickets,car rentals) and cash for most everything else (small hotels, small restaurants, groceries, admissions, etc.). If you let them charge you in dollars, they add a fee - essentially an exchange booth fee - to your purchase.
Complete unity indeed! Always use local currency. Nigel, please be more clear in the future ;-)