If you plan to travel by air between Chile, Argentina, Uruguay and Brazil, you should consider buying a Mercosur Air Pass. The pass allows you to make two stopovers in each country, with a maximum of 10 stopovers. The pass is god for 7 to 30 days. Prices are based on mileage covered. You must buy the air pass outside of South Ameria, and your initial flight must be on Aerolineas Argentinas, American, Continental, Delta LAN Chile, TAM, United.
LAN Chile and American Airlines have joined forces to create the Visit South America Airpass, which allows you to travel between Argentina, Bolivia, Brazil, Colombia, Chile, Ecuador, Peru, Venezuela and Uruguay. You must purchase a minimum of three flight segments, but you can travel for 60 days or less. Again, fares are based on distances travelled. You must buy the pass in your home country.
Internal Brazil flights are notoriously expensive, so it is a good idea to get a Brazil Pass, which allows you to take a few internal flights and it is cheaper than purchasing tickets separately.
Buses are the main form of land transportation for much of the continent. It is possible to travel from Venezuela all the way to the tip of Argentina by bus. In fact, for most South Americans, buses are the main method of transportation. However, it is hard to find direct international routes. Usually, you take a bus to the border, where you must switch to a bus owned by a company in the country you have just entered. From there, you may have to take a bus to the largest nearby city, where you then can switch to a bus to your final destination. It is not the most efficient way to travel, but it is certainly cheap and a great way to see the countryside.
There are no cross-country train services in South America. In Peru there is a well functioning train service with several classes of service on scenic lines running between Machu Picchu and the Sacred Valley, Cuzco and Puno on Lake Titicaca. Also you can travel many Chilean areas south of Santiago on excellent, well maintained trains. Also Argentina has a train service. There are a number of very scenic "tourist trains", including the 445 km Quito-Guayaquil route in Ecuador.
In general, the roads in South America are often in very poor condition, and getting around in a hired car can be dangerous and inconvenient. Taxis are inexpensive except where there are many tourists, like beach resort zones. You can often hire a car and a driver for the day for the same price or less than renting a car on your own.