At the founding of Rome, the gods were numina, divine manifestations, faceless, formless, but no less powerful. The idea of gods as anthropomorphized beings came later, with the influence from Etruscans and Greeks, which had human form. Some of the Roman Gods are at least as old as the founding of Rome.
The concept of numen continued to exist and it was related to any manifestation of the divine. For the Romans, everything in Nature is thought to be inhabited by numina, which explains the big number of deities in the Roman pantheon, as will be shown. Numina manifest the divine will by means of natural phenomena, which the pious Roman constantly seeks to interpret. That's why great attention is paid to omens and portents in every aspect of Roman daily life.
A groups of twelve Gods called Dii Consentes is especially honored by the Romans:
These are the ones listed by the Poet Ennius about the 3rd Century, B.C.E.. Their gilt statues stood in the Forum, later apparently in the Porticus Deorum Consentium. As there were six male and six female, they may well have been the twelve worshipped at the lectisternium of 217 BC.
A lectisternium is a banquet of the gods, where the statues of the gods were put upon cushions, and where these statues were offered meals. The number 12 was taken from the Etruscans, which also worshipped a main pantheon of 12 Gods. Nevertheless, the Dii Consentes were not identified with Etruscan deities but rather with the Greek Olympian Gods (though the original character of the Roman Gods was different from the Greek, having no myths traditionally associated). The twelve Dii Consentes are lead by the first three, which for the Capitoline Triad. These are the three cornerstones of Roman religion, whose rites were conducted in the Capitoleum Vetus on the Capitoline Hill.
But what better characterizes the traditional Roman Religion is the household or family cult of the Dii Familiaris. In this cult, the Lar Familiaris (guardian spirit - Genius - of the family), the Lares Loci (guardian spirits of the place where the house is built), the Genius of the paterfamilias (House-Father), the Dii Penates (patron gods of the storeroom), the Dii Manes (spirits of the deceased) and a multitude of other domestic deities are daily worshipped by the members of the family. The household cult is so important that it even serves as the model for several practices of the state cult (e.g. there were the Lar Praestites, Penates Publici, etc.. Even during the Empire, the Imperial cult came to be based on the household cult, now interpreted as the cult of the Genius of the Emperor, paterfamilias of the family of all the Romans).
Other important Gods are
There is also a group of mysterious deities formed by native tutelary deities, river Gods or deified heroes from Latium which are collectively called Dii Indigites (e.g. deified Aeneas, Faunus, Sol Indiges, Iuppiter Indiges, Numicus). A multitude of other deities is also traditionally worshipped, which includes tutelary deities (e.g. Roma, Tiberinus), native Latin deities (e.g. Bellus, Bellona, Liber, Libera), abstract deities such as Fortuna (Fate), Concordia (Concord), Pax (Peace), Iustitia (Justice), etc.. Pre-Roman native italian deities mainly adopted from the Sabines and Etruscans are also worshipped: Nerio (Sabine deity and the consort of Mars), Dius Fidius (Sabine as well), etc. In fact, Quirinus and Vertumnus were also adopted respectively from the Sabines and Etruscans. The Dii Inferi, Gods of the Underworld (Inferus) are Dis/Orcus and Proserpina, equated to the Greek Gods Hades/Plouton (Pluto in Latin) and Persephone. These Gods symbolize the creative power of the Earth which provide human beings the means for subsistence (Dis = wealth = Plouton in greek). The Inferus is also traditionally regarded as the home for the spirits of the dead, though the concept of afterlife was quite varied.
The pious spirit of the Romans consists of a constant wish to bring the favour of the divine upon him, the family and the state. As such, the Roman is naturally willing to pay the deserved homage and sacrifice to foreign deities, specially if he is in their land. In order to achieve victory in war, the Romans often asked the favour of the Gods of their enemies, paying them sacrifices even greater than those offered by their own people. This spirit joined by the affluence of foreigners which resulter either from trade or conquest, brough new cults to Rome. These were as expected democratically adopted by permitting the priests of these Gods to establish temples in Rome. Among the foreign deities, the Dii Novensiles, are Apollo, Ceres (these were adopted as early as to allow them to become part of the Dii Consentes), Bacchus/Dionysus, Sol Invictus Elagabalus, Isis, Serapis, Cybele, Attis, Mithras and many others.