Richard your observations are correct. No one uses travelers checks here or there anymore. If you found someone here to sell them to you, no one over there would cash them, and you'd be lucky to find anyone under the age of 60 who would even know what they are. People travel there as you would here in the US - credit cards, debit cards, and cash.
But you made two over-generalized conclusions. Not every country uses euro, some still have there own currency so you have to know what they use where you are going. Also the general advice is to use your debit card to withdraw cash over there, just as you do here. There are things you need to know about using your credit card over there. Take a look at the Travel Tips button on the menu on the left of this page, and under that, Money Tips. That will give you a good overview.