Travelers cheques can be quite a pain to convert, plenty of places don't take them, and those that do charge commission that's higher than the rate you get from an ATM. I guess it wouldn't be a bad idea to have a couple on hand, but we've been living in Europe for the last three years, and use our ATM cards everywhere.
The ATM will give you money in the local currency, be it Euro, pounds, crowns or whatever, so in the non-Euro countries you might want to be a bit more circumspect about taking out more than you need - you don't want to get dinged for taking it out and then again for converting it to something else! Within Euro countries, of course, it doesn't matter if you have a bit left over at the end of one country. You would have to figure your exchange rate in before making the withdrawal (ie, if you have a limit of $400/day, you can't take out 400 Euros, but you could take out 300), then your bank would make the conversion and deduct that amount from your account, plus whatever ATM fee they have. So you will only get charged once, by your bank, and at a good rate.
The exchange rate through an ATM is usually the best you'll find, and if your bank charges a fee for using the ATM, it's still less than the commissions you'd pay at an Exchange or on a traveler's cheque. Again, we did almost all our banking during our two years in Lithuania through the ATMs, never had a problem, and found the exchange rates reasonable. In fact, we had a few times when we had to go through ornate bank transfers, and it cost a ton more than just taking the money out through the machine.