In 45 BCE, the Julian calendar first took effect.
In 1673, regular mail delivery began between New York and Boston.
In 1797, Albany replaced New York City as the capital of the state of New York.
In 1801, the first known asteroid, 1 Ceres, was discovered by Giuseppe Piazzi.
In 1818, Mary Shelley's novel Frankenstein, or The Modern Prometheus is published.
In 1863, the Emancipation Proclamation took effect in Confederate territory.
In 1892, Ellis Island opened up to begin accepting immigrants to the United States.
In 1898, by an order of the state legislature, New York City annexed land from surrounding counties, creating the City of Greater New York. The four initial boroughs, Manhattan, Brooklyn, Queens, and The Bronx, are joined on January 25th by Staten Island to create the modern city of five boroughs.
In 1942, the Declaration by the United Nations is signed by twenty-six nations.
In 1966, MTA New York City Transit workers started a 12 day strike.
In 1985, the Internet's Domain Name System was created.
(Sources: Wikipedia: January 1 and This Day in History: January 1.)