I use my American Express card a lot. I have traveled to many places and every hotel i have stayed in has accepted American Express.
As Mmike said, cruise ships will accept all major credit cards.
Carnival Liberty New Year's Eve 2007
Liberty of the Seas 5/2008+11/2009
Allure 1/16/ 2011
Independence of the Seas 12/29/2013 Top-notch!