If someone is money-poor, time-rich, what are the cheapest ways to travel halfway or the whole way around the world?
For example: Starting in Australia or South America traveling to Northern Europe, with a time to get there of 1-4 months.
On continents: Walking and hitchhiking ought to be the cheapest as far as raw transportation costs are concerned (but if it takes longer to cover the same distance, you also have to budget more for food and lodging). Depending on the location, long-distance busses, collective taxis or car sharing are options you can consider next.
Between continents: Air travel, hands-down. If you are flexible with the route and time and look for the cheapest fares or discount carriers, it beats anything else. We often get questions about getting a on a freighter ship or that kind of things, that's possible but not cheap by any means.
Avoiding the most convenient direct flights does save money but beyond that being time-rich does not help you much. Obviously hitchhiking your way across a continent is an experience in itself but there is no secret way to cross oceans or cover long distances and air travel is currently very cheap (historically speaking).