Did they? Yes, at times. As a rule? No.

As the original city-state expanded, the term "Romans" quickly came not to mean citizens of the city but citizens of the kingdom/republic/empire. This included those who were conquered by the Romans during their expansion. Citizenship did not mean equality, as there was still social stratification (patricians versus plebeians), but it did mean "that an individual lived under the 'rule of law' and had a vested interest in his government." [2]

Following conquests, the Romans would engage in a process of cultural appropriation/assimilation. As polytheists, recognizing external gods was very simple. There were restrictions on what they could and could not do, and some land from the conquered territories was redistributed to Roman soldiers following Gaius Marius's reforms, but by and large the people would be left to themselves as long as they respected Roman sovereignty. Eventually, many of these conquered peoples saw the social and economic advantages of becoming Roman, even demanding the opportunity to do so from the central government in Rome.[3]

As a counter example, the Romans certainly engaged in an extermination of their long-time rivals, the Carthaginians, following the third Punic War. It could be argued that this was the earliest recorded genocide.[1] Rome famously (and apocryphally) salted the lands around the destroyed city to prevent it from ever being capable of supporting another society to challenge Rome. However, this was a response to a long-standing rivalry, not the typical territorial expansion.

[1] http://gsp.yale.edu/sites/default/files/first_genocide.pdf [2] http://www.ancient.eu/article/859/ [3] https://www.quora.com/Once-a-territory-had-been-conquered-how-did-the-Romans-treat-the-native-inhabitants