Examples for a territorial acquisiton can be seen in the Mexican-American and Spanish-American Wars, with both ending in the annexation of new territories to the USA; while the use of a sphere of influence can be seen in the Venezuelan Crisis of 1902-1903, the building of the Panama Canal in 1903, and the interventions in the Caribbean (Nicaragua, Dominican Republic). The principal reason for the sphere of influence policy was first that the USA did not intended to maintain an empire as the European powers (in fact many condemmned the annexation of Hawaii and the Philippines) for, to the public imaginarum, the USA was, and still is, a non interventionist-imperialist power, and more of a democratic, liberty guide. More prosaic, the cost of mantaining colonies was a deterrant, with the US government deciding the infuence of the USA was more effective through economic means, but not ruling out military intervention.
This was the reason for the issuing of the Corollary after the beforementioned Venezuelan  Crisis, asserting the new fact of the USA as the dominant power in the region. The Roosevelt Corollary manifest that the USA was the ultimate arbitrater between the European powers and the Western Hemisphere republics, therefore it manifested an interventionist view, rather than a "brotherhood" which can be seen as the original sense of the Monroe Doctrine.
Race and democracy were a key factor of the US policy, as an eurocentric and eugenesic view of the political process was the rule. This was reflected on the contempt of the Latin American countries, viewing them as "degraded" due to the mixing of races, and justifying the instability of their political institutions with that argument, mixing this view with a paternalistic trait, which was the inspiration for the "Big Stick" policy of Roosevelt.
The United States did not helped establish democracy in Latin America primarily because it profitted from the lack of it. This was mirrored in the Caribbean basin, Central America and Mexico. It was not a conspiracy, but American companies profitted better with the autocrats that ruled this republics, and even after American intervention, the goal of foreign policy was "stability", which in many cases lead to the support of Strongmen (Porfirio Diaz in Mexico, Manuel Estrada Cabrera in Guatemala) or direct intervention (the Banana Wars in Haiti and Nicaragua).
Latin American republics responded to this imperialism with both collaborationist and resistance movements.. The first was seen in Mexico and Guatemala (the strongmen lended lands and military grants to the US) while in Nicaragua and Haiti resistance movements were born (Augusto Cesar Sandino in Nicaragua being the most famous).
If one seemed to work was the creation of dictatorial regimes, which were perfected in the 1930's, when strong autocrats infested Latin American (and specifically the Caribbean and Central American Region). Leonidas Trujillo in Dominican Republic, Anastasio Somoza in Nicaragua, Jorge Ubico in Guatemala, Papa Doc Duvalier in Haiti. This "stability" gained through collaboration with the US imperialism and autocratic power was one of the reasons for the use of the "Good Neighbor" policy by Franklin Roosevelt. This was the last act of the reassertation of the sphere of influence policy.
