It was the first oligarchic republic that governed over such a large variety of cultures for such a long time, relatively peaceably. A strong military base was used to keep the oligarchy in power.
The territorial growth of the republic was due to the subjugation and vassalization of neighboring tribes and civilizations.
Economic growth largely benefited the oligarchy, by the time of Julius Caesar, Senators usually owned enormous swaths of land farmed by peasants called latifundia (this was the basis for the feudal system).
This also led to a dramatic increase in the number of slaves and subsequently freedmen. Eventually the patricians (rich people from whom the Senate was chosen from) had slaves for every little thing like opening doors or helping them to dress, etc.
The reforms of Julius Caesar helped the Republic move away from the impending problems of the system and Octavian Thurinas' effective abolition of the Republican system greatly reduced the corruption among the Senators.
The modern democratic nations borrow heavily from this system of government, such as restricting the election of Senators/MPs to only a select group of individuals (oligarchy) as opposed to anyone (democracy). Most of the successful modern democracies also had early territorial expansion by the use of powerful military system, while the more powerful nations (whether truly democratic or otherwise) also create puppet states such as Russia, China and USA.