For a long time, the world celebrated the New Year's in March, as spring ushered in a time of renewal. This makes pretty good sense. Some cultures still do. So why don't we?
Well, we need to go back to Roman times for that. They too celebrated New Years in March, all the way up to 46 BC, that was when Julius Caesar made it January 1st. He did this because the Romans made so many changes to the calendar (the reason that September, October, November, and December are no longer the same number of month that they claim to be). By making it in January, he put the days back in order with the sun. I'm not quite sure how that is, but the Egyptians and Celts thought it was a good idea, so they continued it.
Using a baby to represent the new year is also Greek in origin. They began doing so in 600 BC. I can't seem to find any myth associated with it, but it seems odd that Cronus would fit in as Father Time and there not be a mythical baby for the new year. I would think Eros, but I haven't found anything on that yet. If anyone knows, please post a comment (you can post one even if you don't know - I like reading them).
As far as making resolutions on New Year's Day goes, that came from Babylonian tradition. It started with giving back things that were borrowed but forgotten to be returned. Over time, it changed to making promises, possibly as lazy people probably didn't return things but instead promised to do so in the upcoming year.
So Happy New Year to all of you. My resolution? To try to keep this blog up to date - I did get a little netbook for Christmas which might make it easier, but with a new baby on the way, I'm not holding my breath.