In Japan, there is a custom called "Otoshidama," or New Year's money, which is given to children on New Year's Day.
I think it is a good custom because children can learn how to spend money.
There is also the custom of Hatsumode (New Year's visit to shrines). People go to shrines on New Year's to pray for peace and tranquility for the year ahead.
I also went to Hatsumode with my friend yesterday, and it was a good exercise.