Stay away from traveler's cheques if going abroad. The number of places that take them is shrinking all the time...pretty soon it will be limited to AMEX locations and a small handful of tourist currency exchanges. In many areas, it already is.
I stick to my credit cards. But I ALWAYS call the number on the back of each and every card to tell them of my travel plans in advance. I've had my cards "blocked for fraud protection" while abroad and it's incredibly frustrating!
I bring US$200 in cash for most trips (especially to places that also take US currency). For places that don't also take US$, I try to keep a small handful of local bills/coins for tips, a drink, etc., upon arrival. But I try to use plastic for absolutely everything possible.
NO debit cards. Ever. Keep them in your hotel safe or other secure location. I never touch overseas. If you stick to places that take credit cards, and also carry enough cash for places that don't, you shouldn't need to go to ATMs. NEVER use debit cards for POS purchases (i.e. like a credit card). It's just begging for your money to disappear, with little recourse to get it back (unlike a credit card where you don't pay until you can review the charges).
One word of warning: Do NOT make online purchases while connected from ISPs in the foreign country. It's a surefire way of getting your cards blocked! (they trace the IP origin) Instead, look up what you want online, then call the 800 number via Skype to place the order--it's free even if you don't have a subscription.