From an Eskimo village in Alaska. Don't remember which one, as I visited several on that trip. Had to walk about a mile across the tundra on a wood plank walkway to use the only phone in the village at the general store.
Crab Meadow Beach, North Shore, Long Island using DBC's QuoteTrek FM Reciever and a payphone. This is early 90's trading options.
On my phone in a small island (Bantayan island) off Cebu City, Philippines. The island barely had any electricity but I had GSM/GPRS working on my blackberry
Closed some forex positions using GoToMyPC (to access my home computer in Chicago) from an old desktop in a friend's apartment in Nanchang China. Not "exotic" but it got the job done.
korean bar/niteclub... they have pcs in bars ... it was market hours in nyc, nite in seoul. just had to make a trade.