So, you want to see the world? There are, obviously, scads of ways of doing it, but one of the cheapest is to purchase a round-the-world ticket. But how do you cull out the values from the scams?
Two services come highly recommended. One World Alliance calculates your fare by the number of geographic regions you visit.
Star Alliance is a more straight-forward mileage-based system, reportedly a better deal if you're tracing a more-or-less straight line around the planet.
Finally, Lonely Planet (which is an excellent resource for independent travellers) offers not only links to a number of global communications, banking and booking services, but also a "multi-stop airfare" calculator which runs off a point-n'-click map. It's the easiest to use, but the fares it generates vary wildly. The scuttlebutt is that you're best off using LP as a place to daydream, make plans and pick up tips, while actually buying elsewhere.