From Montevideo to Buenos Aires
A very common trip is to go from Montevideo to Buenos Aires or the other way around. You can choose between going by bus all the way, going by bus to Colonia in Uruguay and then by ferry to Buenos Aires, or taking a direct ferry from Montevideo to Buenos Aires.
Bus
It is possible to go all the way overland with buses, e.g. with the companies Bus de la Carrera and Cauvi. However, when you have a quick look at a map you will realize that taking a ferry to cross the Rio de la Plata is an enormous short-cut and going overland takes and additional 5 hours of travel time.
It should also be mentioned that in the past some of the bridges connecting Uruguay and Argentina were frequently blocked by "piqueteros" and environmentalists protesting against a paper plant in Uruguay. However these issues are resolved and the buses circulate without problems as of 2013.
A reason to go all the way overland could be the lower price tag and also a more convenient travel experience in case of bad weather: the fast ferries crossing the Rio de la Plata will then start to roll unpleasantly in response to the waves. Bus services start at the terminal Tres Cruces in Montevideo and arrive at the terminal Retiro close to the centre of Buenos Aires.
Bus and Ferry
A recommendable and popular possibility is to travel by bus between Montevideo and Colonia, and by ferry between Colonia and Buenos Aires. The bus segment takes about 3 hours, and a fast ferry an additional hour. That way you can watch the Uruguayan landscape on your bus trip and also have the option to stop for a couple of hours to visit Colonia, which is an interesting destination in its own right. Note that the ferry operators do also operate their own buses, so there is no organizational effort needed from your part.
You can choose between the companies Buquebus, Colonia Express, and Seacat Colonia. The buses usually depart from the terminal Tres Cruces in Montevideo and the ferries arrive at their respective ports in central Buenos Aires (close to the bus terminal Retiro in the case of Buquebus). A different choice is the smaller ferry company Cacciola which operates between Carmelo in Uruguay and Tigre in Argentina.
Ferry
Buquebus is the only company that offers a direct ferry service from Montevideo to Buenos Aires. With three hours of travel time it is about an hour faster than the combined ferry and bus trip via Colonia, and it is slightly more expensive.