When I backpacked around Europe, I brought very few traveler's checks (they are a real pain) and relied instead on my ATM and credit cards. But do be sure to bring $200-300 in cash with you, just in case (that's my opinion).
I recommend changing at least half of that cash into the currency of the country you're arriving in, BEFORE you leave, because you are going to need some cash as soon as you arrive and you don't want to exchange it anywhere near where tourists are known to linger (airports, train stations, etc).
And of course, you'd better be carrying all of this in a travel-wallet thingy that stays right next to your body. I have a "money belt" that I have worn on every international trip, and it never leaves my skin unless I'm in the shower (and it's usually hanging in the shower with me, if I'm in a hostel). It holds my passports, ID, plane tickets, contact info, and all money-related things.
That said, tuck a US$50 into a small pocket on your backpack or in your sock every morning, or something. You never know when you might need it, if all else is lost. The idea is to spread out your risk of being mugged/robbed.
(Sorry if I'm a little paranoid, but I have seen all kinds of shit when traveling internationally... people do stupid things, and there is ALWAYS someone to take advantage of you when you're a foreigner doing something stupid.)
