Marie and Emma,
I can only speak to Ecuador, though I was there just a few weeks ago. PA makes good points and I would generally follow them all. In fact, while I've had no troubles, I wish I would have gotten a second debit card just in case. Too late now, of course.
In Ecuador, ATM's are plentiful. I found the ones with Banco Pinchincha (spelling may be a little off) didn't charge me a fee to use the ATM...my bank did, but that's another matter.
Be sure to ask your bank and credit card companies about service fees and foreign transaction fees. It could add as much as 1-5%!t(MISSING)o every purchase you make.
I wouldn't use traveler's cheques...they will be difficult to impossible to cash.
Speaking of cash, Ecuador uses the US dollar as the official currency with their own coins - but all correspond to U.S. coins (i.e. a one cent piece, 5 cent, 10 cents, 25 cent, and also a 50 cent piece. They also use the golden Sacagawea dollar coins that Americans won't use, even if they are legal US dollars). That said, it was my experience it is hard to make change in Ecuador. I would get/bring a fair amount of small bills such as 1's and 5's. You will need them. Don't use 50's or 100's, nobody will accept them. In fact, they get suspect of $20 dollar bills. You'll see them holding them up to the light for the strip though the bills and using the counterfeit pens on $20's and sometimes even $10's. Be sure to note, even banks don't like to give change for $10's and $20's...all the more reason to bring small change. That said, if you're at a restaurant and all you give them is a $20 after you ate the food, they won't have much choice but find change. You may just have to wait until they go down the street to another business to find change...or you may end up giving a big tip.
I would also plan on using cash for most purchases in Ecuador. Relatively few places take credit cards because the banks charge very high commissions to use credit cards (such as 6-8%!o(MISSING)f the purchase). You may find if you want to use a card (and a business will accept them), they will add 6-10%!t(MISSING)o the bill. About the only places that took cards without much hassle were the biggest businesses, such as the big hotels, some restaurants in Gringoland (La Mariscal) if you had a minimum amount of purchase, and the airlines.
Hope that helps on at least Ecuador. I found it a spectacular country to visit and want to go back sometime soon.