Amazing Grace (1773)
The words to what would become the hymn “Amazing Grace” (arguably the most popular English-language hymn) first appeared alongside a sermon (it's unknown if it was accompanied with music). Though written originally for an English parish, its popularity really took off in 1800's America.
The New York Ball Drop (1908)
This was the first time the ball dropped in Times Square (technically starting a minute earlier in 1907) to welcome the new year. It was introduced to replace a fireworks show previously held by The New York Times newspaper. It has dropped every year since (except 1942 and 1943).
The First January New Year (45 BC)
In this year the Julian calendar took effect, making January 1st the official start of the year. Julius Cesar devised the calendar to have twelve months and three-hundred and sixty-five and one quarter days (accounting for leap years).
First Coast to Coast Color Broadcast (1954)
America was the first country to use color television broadcasts, having done so in 1950, but it wasn't until New Year's day in 1954 when NBC broadcast the Tournament of Roses Parade all over the country. New types of televisions were produced to show this new technology to the public.
The most famous New Year of them all, the Y2K bug was an issue relating to how computers understood dates. Essentially systems that understood years with two digits could mistake 2000 for 1000. This promised to wreck everything. Then January 1st rolled around and nearly nothing happened. Though some computer issues are documented, the most far-flung fears never materialized.