All inhabited continents have some sort of bus travel and unless government regulations or geography prohibit it, you can find some – at least nominal – bus service almost anywhere you go. While comfort and prices range wildly, from the infamous chicken buses, the engines of which may or may not survive the next steep ascent, to luxury buses in countries such as Saudi Arabia, buses are usually the cheapest option at least on short distances.
Contrary to rail, which is usually organized at the national level, it is often easy for anyone to start a bus company. Where regulation is absent or moderate, there will thus be many independent firms, not always coordinating very well. You often have to check the connections locally.
There may also be a few dominating companies. National monopolies or cartels are rare, but in some countries government regulation sets (usually rather low) prices and/or pays subsidies, thus establishing a quite stable market. Still competition often varies from route to route. You will not have much trouble finding a company that goes from Washington DC to New York City, but a trip from Herzogenaurach to Regensburg may only be offered by a single company or none at all as a direct route.
Where there is a need for public transport, but no economically viable market, there may be heavily subsidized taxis or minibuses for the target audience, still taking outsiders as passengers – to find these you may have to get local advice even in places where most timetables are on the net. School buses sometimes belong to this category (and you might be able to go in the reverse direction as well).
Some main categories of buses are:
Depending on the line, tickets may have to be bought in advance, paid to the driver or paid to a separate conductor. On some lines it is possible to reserve seats.
Something being announced as a bus route does not necessarily mean you will ride a bus. In some regions you may end up in a lorry and where passenger volumes are small you might have to board what looks like a taxi. Also, bus stops are not always well marked or marked at all.
Bus operators have different attitudes towards standing passengers. While it is par for the course on chicken bus, laws and regulations in other places may require not only sitting down but buckling up. In some countries a few buses at the lower end of the price scale may transport standing passengers even over long distances, but the "first class" buses on major routes may not even fill all seats or seat less than the standard 2 + 2 (two left and right of the aisle).
For long bus rides you may want to have a bottle of water, something to eat (eating not allowed in all buses, though), something to read and perhaps something to lean your head against if getting tired. A map and guidebook, with which to keep track of what you see, is also good to have. On some lines there are newspapers, coffee and snacks available. If you are prone to get carsick, avoid seats in the rear end, try to get a seat with a good view, avoid reading or looking at your tablet for longer moments, and have a plastic bag handy. If you are travelling with children, having food, entertainment, paper towels etc. may be crucial. Unless there is a functional toilet, you should use the breaks (but do not miss the bus). If you aren't getting off at the very last stop, it is usually a good idea to try and tell other people on the bus, especially the driver or conductor, where you have to get off. In many instances, stops are "on demand" only or in non-obvious places and you may only recognize the landmarks of the city you want to go to when the bus is already pulling out of the station.
Capacity for luggage varies. On some buses you will want or have to have your bags on your lap, in some there is an overhead rack for smaller bags, in some there is a luggage compartment below or behind the passenger compartment, in some the luggage is fastened on the roof. You may want to have your most important belongings in bags small enough to keep with you even in a crowded bus.
Almost all buses are designed for top speeds no higher than 110 km/h, some don't even reach 80 km/h. In some countries, e.g. Germany, this is enshrined in laws and thus technical developments in favor of higher speeds are unlikely. This means in practice that, all else being equal, trains are faster than buses almost everywhere where railways are up to a 21st century standard. (However, bus departures may be more frequent and have more convenient stops). In low income countries some buses are even slower and the ubiquitous former US school buses sometimes have trouble getting up hills. Still, bus drivers – especially those of "minibuses" – are notorious for driving aggressively, even if that might seem "suicidal" to outsiders. Be assured that especially when there has been a delay and time has to be made up, the driver will do anything in their power to get the lost time back. Another factor often limiting travel speed is the state of the roads. Sure, the Caribbean Coast is only a few hundred kilometers from Managua, but the roads are often nothing more than a small stretch of dirt that has been (mostly) cleared of trees and undergrowth and even at the maximum speed the bus will do on such routes you can easily spend a day or more on the road. If you take a ride such as these, you will surely have a tale to tell, but you might want to reconsider taking a bush plane on the way back, especially if the bus does not in fact make it and you have to be picked up by the next one.
While some bus companies have perfected "at your seat service" to an art form, and others have roving vendors for everything portable, buses in other regions may offer a limited selection only or nothing at all. Bringing your own is always a good idea, especially on long routes. This is also true if the bus makes scheduled "lunch breaks", as those are often at overpriced venues exploiting a captive market. Don't get yourself into a situation where you have to spend $20 on a two-day-old sandwich or go hungry for the next eight hours. Choose food that won't make a mess and won't fill the cabin with an odour. Read up about the bus company you're travelling with to learn about the services they provide, if any.
In some regions one is always supposed to share ones food or snacks with those nearby, at least among the ones sharing a bench. It is generally polite to accept a small amount of what you're offered, even if you don't really want it.
A long bumpy bus ride is often the ideal way to meet locals and strike up conversations with "real" people. Except tour buses and other services which cater to an international crowd, language barriers can be expected (do not forget to bring a phrasebook).
Sleeping restfully on buses can be difficult – it's easy to end up exhausted after an overnight bus from one city to another. But if you can master it, it's a way to both save money on lodging for a night and also use your waking hours to enjoy your destination instead of spending them on transportation. A few recommendations:
Though not as common as sleeper trains, buses specifically designed for sleeping passengers do exist in some parts of the world. These range from seats that recline extra-far to honest-to-goodness bunks with pillows and blankets. These are often more expensive than a "regular" bus. If you find the increased comfort worth the price difference, by all means go for it.
Wikivoyage has guides on bus travel in some countries where this phenomenon is either widespread or rather new. If you know about a country Wikivoyage should cover but does not, please plunge forward and create the article. For many countries the issue is more briefly handled in the "Get around" sections.
City buses are a high-risk area for pickpockets, who can take advantage of packed crowds, noise, and travellers' confusion. Long-distance buses tend to be safer in this regard, as they are usually less packed and fewer people wander on and off the bus in a short time, but still keep an eye on your luggage. In general buses are less safe and more prone to accidents than trains. Buckle up where seat belts are available.
Keep in mind that night buses are likely to be less safe than day buses—this goes for long-distance buses as well as city buses.