The two major credit card networks, MasterCard & Visa, also own the two largest global ATM networks, Cirrus and PLUS (respectively).

Most banks in the US have affiliation with either network....Bank ATMs around the world are required by MasterCard and Visa to display signage on the ATM of which networks they accept (usually both).

In my global travels, have never had to carry travelers cheques and only relied on my Chase or Citi issued ATM card. No problems at all except in Brazil....then I just had to go to a Citibank branch.