I do not recommend Citibank's "Global Executive" banking. Open 9 to 5 Monday through Friday New York time, and the call is often routed to India anyway. (Not that there's anything wrong with India per se, but then what's the point of such limited hours for the "Global Executive"?) The Citi never sleeps indeed! Absolutely awful service. I ended up closing the account after several months. On the other hand, I like Citibank Japan as a local bank.
There are some U.S. Internet-only banks that may work well nowadays for the world hopper. Everbank.com is an example of an online bank that allows you to keep deposits in multiple currencies. This Web site seems like a good place to start comparison shopping for Internet banks:
http://bankdeals.blogspot.com