Unless you're on a yacht sailing between Fiji and the Marshall Islands, you'd really have to make a big effort to find yourself on one of the Tuvaluan islands. Tuvalu (formerly the Ellice Islands) is variously declared the second, third or fourth smallest sovereign nation in the world and, according to the UN, is one of the least developed.
If you're a harried city-slicker wanting to disappear for a while, you could do a lot worse than head to Tuvalu. On average, it receives fewer than 1000 tourists a year (most of them as part of foreign aid delegations), has little or no natural resources, boasts few natural wonders, is difficult to get to and nigh on impossible to get around in. As a result, it's not exactly number one on most travellers' lists of 'must see' locations. This might sound like bad news, but if all you want to do is sit under a palm tree and never be bothered by anyone, you're in luck. Get in quick, though. Millions of dollars of new-found income and rising oceans are vying to swamp Tuvalu in the near future.