Round the world overland
Traveling around the world has been a goal for many intrepid explorers ever since humans suspected that the world was round. Ancient Greek mathematicians calculated that the world was round and speculated on how to follow it all the way. The first persons generally acknowledged to have pulled off this trip were the survivors of Ferdinand Magellan's crew. With the widespread deployment of locomotives and steamships in the late 1800s, Jules Verne predicted a trip around the world in eighty days to be feasible by land and sea.
These days, it is easy to buy a number of flights that take you around the world, but many people choose not to fly. One reason is that air travel is a polluting form of transport. Another is that the joy of traveling is the journey itself and the many places and experiences that come from passing through countries rather than flying over them.
Many people plan to travel around the world without using air transport by using a combination of sea, rail and road, although generally it is almost impossible not to include some air transport on the way, due to the cost of covering the oceans and for political reasons in some parts of the world.
In a nutshell: the very minimum requirements for a trip like this are several months of time, good health and, expressed in American dollars, a five-figure sum of money.
There are a limited number of arranged overland trips around the world. In practice these trips are cruises circumnavigating the globe from port to port, therefore a more describing name for them would be "over seas". Some travel agents arrange places on freight ships going around the world, the rest on regular cruise ships. These usually last about 100 days, and prices begin at USD 15,000.
A few cruise ship lines package a "world cruise" as a single bundle, with duration typically 110-120 days. These trips typically run once annually.
On your own
A possibly cheaper and definitely more adventurous way is to combine scheduled intercity bus, train and boat connections to go around the world. You plan your trip from scratch and set your own schedule - however this will mean a lot more planning than eg. flying round the world through ten cities. Remember that your itinerary will very likely include places far off the beaten track and far away from everything. Consult the articles for each of the countries you plan to travel to in order to learn about the connections and travel conditions.
Crossing from Europe to Asia or vice versa can be done relatively easy – you can take a train from most major European cities to Moscow and travel by the Trans Siberian to Beijing. Travel through Central Asia or Middle East is possible but requires more visas and more changes of buses and trains.
The Pacific Ocean is by far the greatest obstacle to completing a circuit around the world overland; There are no ferries between either Indonesia or New Zealand to Australia, nor are there any sort of regular services from Asia or Australia to the thousands of islands in Polynesia. Further north the Bering strait between Russia and Alaska doesn't have any scheduled traffic crossing it either. Moreover there are no roads on either side of the Bering Strait and a special permission is required to enter Chukotka on the Russian side. This means you either have to shell out more money than a plane ticket on the cruise ships that do cover this route – Japan to Alaska is the most economical option – or opt for the option more in the spirit of such a journey; Freighter travel. New Zealand, which maintains loose associations with a number of small islands in the Pacific, sometimes offers for people to join on the semi regular freight routes, supplying these islands, but natives are always given priority, and securing a spot on these trips are not trivial, and requires much perseverance. If you want to cross as many longitudes as possible by land but are willing to fly if absolutely necessary, things get a little easier. Coming from Asia, you can get across the Indonesian islands by ferry and overland to the easternmost of Papua New Guinea. From there you can fly to New Zealand, via Australia if you wish. The North Island reaches all the way to 178°E. From New Zealand you can fly via Hawaii to Anchorage, Alaska from where you can backtrack by ferry to Dutch Harbor-Unalaska, located at 166°W. Alaska is connected by ferry and road to Canada and the Lower 48.
Traffic over the Atlantic is much more frequent than over the Pacific. Cunard Line's proud historical ocean liners still ply the route between Southampton and New York, and are much more economically feasible than the Trans-Pacific cruises. Some cruise ships spend the summer in Europe and the winter in the Caribbean and offer affordable "re-positioning cruises" across the Atlantic. Lots of freighters cross the Atlantic between Europe and the Americas and journeys on these can be arranged through several agencies. Also quite many recreational sailors cross the Atlantic (see Hitchhiking boats). Yet another alternative would be flying from Halifax to Reykjavík, Iceland, taking a bus to Seyðisfjörður and Smyril Line's weekly ferry to Denmark on the European mainland. Headstrong, experienced travellers with a very loose timetable could attempt to cross the North Atlantic on fishing vessels – Greenland to Iceland is, while in no way easy, possibly doable. But how to cover the strait between Canada and Greenland is not immediately clear, it may be possible to hire experienced Inuit to cross the strait on dog sleighs during the winter.
Perhaps surprisingly, another obstacle is the Darién Gap: a small 160 kilometre stretch of dense marshy jungle, made even more dangerous by guerrillas fighting in the area, between Panama and Colombia. Yes, this means there are no roads between Central and South America, there are no ferries covering the gap either, but backpacker traffic is so heavy that there is a fairly organised line of private vessels operating between Cartagena and the Portobelo Area or Carti in Panama. As of August 2014 the company San Blas Ferry operates a ferry between Carti in Panama and Cartagena in Colombia. It is also feasible to walk along the Caribbean coast line, but unless you have experience in such journeys, this is not something you should take lightly. From Europe you can go by freight ship to Montevideo and some places in Brazil and some of the cruises in the Caribbean also include ports in Venezuela.
Northern Africa can be easily visited from Europe. However, if you want to travel further south overland you need to cross the Sahara desert, which is a challenging task. You could possibly travel along the west coast, passing through several countries that require visas from almost all foreigners. The easier route would be in eastern Africa, sample routes include Cairo to Nairobi overland and Alexandria to Cape Town by train and bus. Rail transportation and paved roads are uncommon, therefore getting around can be challenging and take time. Also, inform yourself about the situation in the areas you plan to travel through – sadly infectious diseases, armed conflicts and crime are prevalent in much of Africa. Finally, to get out from anywhere in Sub-Saharan Africa your alternatives are to either backtrack north to get to Europe or Asia or fly. Crossing the Indian ocean by boat is dangerous because of pirates, at least unless you take a very southerly route.
Australia and the rest of Oceania require flying if you aren't going by freighter or by an irregular and expensive Trans-Pacific or RTW cruise. While most Indonesian islands are connected to each other by ferry and western Indonesia has several connections to the Asian mainland, as of now there are no scheduled ships between Asia and Oceania.
Overall getting from one continent to another in the Southern Hemisphere is in practice an option only if you have your own boat.
Already over 100 years ago a car race from Beijing to Paris was arranged, and in 1936 two guys from Prague drove around the world in 97 days. There are two ways to drive around the world: you can buy and sell vehicles along the way, which means that you can fly over difficult and dangerous regions and don't have any problems getting it over the oceans. If you drive the same car around the world you will have to drive all the way and arrange with freight ships to take the car at least over the Atlantic and the Pacific. Driving around the world means you will need various documents in addition to your passport and visas such as an international driver's license, Carnet de Passage, documents concerning the car's insurances and in some cases even a local driver's license! Weblogs where RTW drivers share their first hand experiences include Transworldexpedition, The world by road and Vw vagabonds.