While everyone assumes that cash is accepted everywhere, there have been times when cash in large denominations is not very convenient. I have had banks in Greece refuse to exchange $50 or $100 bills, but I never had problems with $20 bills.
World wide ATM networks have almost made Traveler's Checks a thing of the past. What they do have going for them is security. They are accepted in most places and shops, especially in areas where tourists frequent, but if you venture off the tourist track, and want to buy a memento or two, you will find that people have no idea what they are, so make sure you exchange them for cash at a local bank.
Even in businesses that take travelers checks, you might have a hard time paying or exchanging large denominations of traveler's checks especially (fifties or hundreds). I have found large bills are treated with suspicion by vendors and some might not accept them. Finally, you never know what exchange rate the merchant is willing to offer. Better to exchanging them for cash at a bank.You should have your passport with you when you pay with traveler's checks to verify your identity.
When you make a withdrawal at an ATM, it disperse Euro using the conversion chart displayed on the bank's window. Make sure you keep all receipts though for a few months after you return home. This way you can review your account and make sure you weren't double charged.