When it comes to bus travel, there are really 3 main types of bus service to consider; long-distance (both national and international), local and jump-on jump-off services (or JO-JOs).
Scheduled coaches running on long distance national and international are many and varied. Although slower than plane and train travel, taking a bus can at times more than make up for this with money saved. In Europe comfort levels can be varied, but have been increasing substantially in the last few years especially in Eastern Europe.
When planning to travel by bus in Europe, Australia, New Zealand and North America you should always look at bus passes to establish whether buying a travel pass will save you money compared to buying a number of point to point tickets. Remember that a travel pass will also offer you increased flexibility compared to pre-booked (but often unchangeable) tickets.
In developing countries buses often provide the only cost effective method of transportation to get around, especially where the infrastructure may be somewhat basic. In some countries, however, the road safety as well as the quality of vehicles may leave something to desired. If this is a concern for you, you may wish to consider an overland tour, where operators can be expected to maintain their vehicles to western standards.
Jump-on jump-off services are an excellent compromise for travellers who want the flexibility of being able to jump on a bus out of town whenever they want, but still enjoy travelling with other backpackers. JO-JO travel means you are guaranteed to make friends when you are travelling and can also offer you added security when travelling in parts of the world with higher incidents of crime (such as South Africa and parts of South and Central America.) Probably the best known of the jo-jo busses is Busabout, which is well worth a look if you are planning travel in Europe.