There was a religion of the family and the farm before a state religion; the former influenced the latter.
Regarding the State religion, at the founding of the Republic the major gods were Jupiter, Mars, Quirinus and Vesta. The first three were served by major flamines (recruited from Patricians), the latter by the cult of the Vestal Virgins (selected among Patrician daughters). There was also a rex sacrorum, king of sacrifices, who seems to have taken over some of the monarch's former religious duties: among other things the rex made sacrifices to Janus, the god of beginnings.
The minor gods recognized by the state were served by minor flamines (Plebians could serve) and they were: Vulcan, Volturnas, Palatua, Furrina, Flora, Carmenta, Portunas, Falacer, and Pomona.
As you can see, most of these gods are local agricultural deities. I'm sure somewhere in the Latin countryside they still had cults among farmers and peasants, but by the late Republic many of the state cults from the monarchy had grown anachronistic, and even the deeply conservative Romans had often forgotten the withers and wherefores of many of their older cults.