Rosh Ha Shanah
Decorations, singing, drinking, dancing: in short, merriment, is what people associate with New Year Celebrations. And this is why a New Year often starts with a headache (which sometimes comes in quite handy for forgetting the monumental resolutions made the day before). Religion normally features only at the brink of it all, if at all. Churches try to change that, by offering watchnight services, or celebrations inside the Church. But no Christian would dare to dream of what happens in Synagogues when a new year comes around.
First of all, there are two New Years in the Jewish calendar (three, if you count the "New Year of Trees" as well), because there is a sacred year, starting at the month of Passover, and a civil year, starting at Rosh Ha Shanah. Both cycles are used for different purposes, which turns biblical timelines into quite a puzzle sometimes.
Second, one complete month (Elul) is dedicated to the preparation.
Third, it starts with a mighty blow from a ram's horn (in the acoustic sense only, but there can be victims of that, too).
Fourth, it is not about making new resolutions, but about checking the old commandments, seeing what has been done about them and what to do now. The result: teshuvah (repentance), tephillah (prayer) and zedaqah (practical charity). For while the biblical reference is Leviticus 23:24, tradition links Rosh Ha Shanah to three other passages, all of which signify a new beginning: the Creation, the birth (and binding for the sacrifice) of Isaac, and the birth of the prophet Samuel. And to start anew, you need a clean slate.
Another tradition says, that on Rosh Ha Shanah, God judges every living being, but the judgement is kept open until Yom Kippur, the day of atonement, when it is sealed for another year. This why the traditional greetings on that day are: "May you be written down for a good year" and "May you have prayed down on you all that is good".