Two-faced Janus (Ianus), presumed to be native to Italy, is the god of beginnings/endings. It's after Janus that the first month of the year, Januarius 'January', is named. The kalends (the 1st) of each month may have been dedicated to him.
Rabun Taylor (citation below) eloquently describes the lack of a coherent story about Janus:
"Janus, like so many ancient gods who lacked the grace of a story, was a messy concrescence of scraps fallen from the table of memory. His incoherence was the cause of some puzzlement in the Roman Imperial era, and so he was periodically subjected to reassessments by master yarn-spinners like Ovid or by cosmologists and philosophers seeking to find profound symbolism in his duality."Janus was not only a god of beginnings and transitions, but was also associated with war/peace since the doors of his shrine were opened except in times of peace. He may have been a god of stream crossings.
Ovid, the Augustan Age teller of mythological tales, provides a story about the early benefits conferred by Janus.
 "'I have learned much indeed; but why is the figure of a ship stamped on one side of the copper coin, and a two-headed figure on the other?' 'Under the double image,' said he, 'you might have recognized myself, if the long lapse of time had not worn the type away. Now for the reason of the ship. In a ship the sickle-bearing god came to the Tuscan river after wandering over the world. I remember how Saturn was received in this land: he had been driven by Jupiter from the celestial realms. From that time the folk long retained the name of Saturnian, and the country, too, was called Latium from the hiding (latente) of the god. But a pious posterity inscribed a ship on the copper money to commemorate the coming of the stranger god. Myself inhabited the ground whose left side is lapped by sandy Tiber's glassy wave. Here, where now is Rome, green forest stood unfilled, and all this mighty region was but pasture for a few kine. My castle was the hill which the present age is accustomed to call by my name and dub Janiculum. I reigned in days when earth could bear with gods, and divinities moved freely in the abodes of men. The sin of mortals had not yet put Justice to flight (she was the last of the celestials to forsake the earth): honour's self, not fear, ruled the people without appeal to force: toil there was none to expound the right to righteous men. I had naught to do with war: guardian was I of peace and doorways, and these,' quoth he, showing the key, 'these be the arms I bear.'"Janus was also an augur and mediator, perhaps the reason he is named first among the gods in prayers. Taylor says Janus, as the founder of sacrifice and divination, since he can see the past and the future through his two faces, is the world's first priest.
Ovid Fasti 1
It was Roman tradition at the New Year to give the god honey, cakes, incense and wine to buy favorable signs and a guarantee of good luck. Gold brought better results than baser coins.
"Then I asked," Why, Janus, when I placate other gods, do I bring incense and wine to you first?" "So that you may gain entry to whatsoever gods you wish," he replied, "through me, who guard the threshold." "But why are glad words spoken on your Kalends? And why do we give and receive best wishes?" Then the god, leaning on the staff in his right hand, said, "Omens are wont to reside in beginnings. You train your anxious ears on the first call, and the augur interprets the first bird he sees. The temples and ears of gods are open, no tongue intones wasted prayers, and words have weight." Janus had finished. I was not silent for long, but tagged his final words with words of my own. "What do your dates and wrinkled figs mean, or the gift of honey in a snow-white jar?" "The omen is the reason," said he - "so that the sweetness replicates events, and so that the year should be sweet, following the course of its beginnings."
Translation of Ovid Fast. 1.17 1-188 from Taylor's article)
Happy New Year!
Source: Janus Photo © Clipart.com
"Watching the Skies: Janus, Auspication, and the Shrine in the Roman Forum"
Memoirs of the American Academy in Rome, Vol. 45 (2000), pp. 1-40
Janus Photo © Clipart.com