I know this is going to be a hard-if-not-impossible-to-answer question, and probably does not have one unique answer, but I do think it is relevant at some level for many people visiting this site.
What is the absolute cheapest means of travel, if the objective of the journey is the journey itself? This means at least the following:
a small amount of people (friends, wife+kids, ...) will be traveling always together
the various destinations are usually improvised, far and widespread. E.g., there is no predefined course or plan to it
The total duration of the journey will be several years
With these constraints, hitch-hiking is out of the question (who'll take on 4-7 passengers? it's unpredictable where you'll end up, e.g., virtually impossible to plan anything, etc.).
I have read many stories about sailing trips with this philosophy. It makes intuitive sense -- sailboats do not require fuel, hence the distance can (when the winds are right) be covered at no cost at all. But somehow I question whether this is true from an end-to-end perspective -- in general, sailboats at the size you'd need them don't come cheap (you'd have to rely on selling the boat when you're "done" traveling), there are costs for harbors around the world, you'd have to bring "special" food that stays well longer, the boat also requires fuel, etc. Plus you'd be kind of limited to islands or places near the shore.
An alternative I thought of would be to travel by car, e.g., buy a cheap car, travel, and sell it again (possibly at higher value). This of course assumes cars are much more easy to sell; not an unreasonable assumption I'd say. The only costs would then be fuel, which is only cheap in the US and some smaller states scattered around the globe. End-to-end, would this be cheaper?
In summary, I'd like to hear reports/stories/etc of the true globetrotters reading this question, regarding the cost of their means of transportation, how they compare, and in the end, which means of travel (or combination thereof) is generally the cheapest.