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.
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 some of the bridges connecting Uruguay and Argentina are frequently blocked by "piqueteros" and environmentalists protesting against a new paper plant in Uruguay. So it may be wise to ask the bus companies about the current situtation and expected travel times. The issue is not yet resolved as of early 2008, and will probably last for some more time. On the other hand you need not worry too much since the bus companies are experienced with this sort of problems and are usually allowed to pass by the protesters.
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.
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 and Colonia Express, both services will start at the terminal Tres Cruces in Montevideo and arrive at their respective ports in central Buenos Aires (close to the bus terminal Retiro).
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.