I've been lucky enough to afford two weeks off in a tropical country each year for the last five years. On all five trips I've left the cell phone and pager at home and stayed at places that don't have television, phones in the rooms or Internet connectivity.
The first time I did this it felt really strange to be disconnected from "the world", but now I look forward to it.
BTW, Fiji has been the best location so far.
http://www.matamanoa.com/