Round the world overland
This article is a travel topic
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.
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.
There are a limited number of arranged overland trips around the world. Some travel agents arrange places on freight ships going around the world, and some cruise companies also offer round the world cruises. These usually last about 100 days, and prices begin at USD 15,000.
There is also a transcontinental bicycle tours company with whom you can cycle from Shanghai to Istanbul to Paris, or from N to S across N and S America, Africa and Australia. Do 2 or 3 of their tours and you will have cycled around the world. See tourdafrique.com for more information.
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 Railway to the Russian Far East (Vladivostok) or China (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. 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.
The Atlantic is much less problematic, as Cunard Line's  ocean liners, still ply the route between Southampton and New York, and there are several cruise lines that offer transatlantic cruises including cheaper repositioning cruises where ships are seasonally moved from Europe to the Caribbean or back again. It is also possible to book passage on a cargo ship, however this is rare. 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, and from Iceland there are regular ferries to the Faeroe Islands and Denmark on the European mainland with Smyril line . It's hypothetically possible to cross the strait between Canada and Greenland on the sea ice but the trip would be extremely dangerous and expensive. One solution would be traveling by ship to Iceland and then taking a bus to Seyðisfjörður and the ferry on to Europe.
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. There are no roads between Central and South America, but there is a fairly organised line of private vessels and a ferry operating between Cartagena and the Portobelo Area or Carti in Panama. See  or  for more information. It is possible to cross the Gap on foot, but unless you have experience in such journeys and an experienced guide, this is not something you should take lightly.
Northern Africa can be easily visited from Europe. However if you want to travel further south overland you need to cross the Sahara desert - don't expect any bus connections as there are hardly any roads. However several overlanding tour companies offer trans-africa trips (There are good bus connections from Egypt and Morocco heading south.)
Australia and the rest of Oceania requires flying if you aren't going by freighter or by an irregular and expensive transpacific or RTW cruise. There are several shipping companies that offer berths from Singapore to Australia and it is possible to join the crew of a private yacht being repositioned to or from Australia although an inexperienced sailor might be charged. Even the above mentioned bus tour from London to Sydney includes a flight leg from Indonesia to Darwin. Overall getting from one continent to another in the southern hemisphere is extremely difficult by 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 .