In Japan, New Year holidays are the busiest period in entire year. Most of Japanese go back to hometown in this season. So the trains depart from major cities, like Tokyo, Osaka, Nagoya will be very busy. Most of companies will be closed from Dec 30 to Jan 3. In this coming season, I expect Dec 27, 28, 29 and 30 will be busy. And everybody come back on January 3 and 4. So you should avoid to take a train on those days. In some of the trains, the occupancy rate may be more than 200%. As long as trains have non reserved seat, you can get on anyway without any reservation. But you will be forced to stay on the isle or passenger’s deck without seat. There are many passengers without seats in the train during those busiest days.
The movie below shows you the station and train in new year in 2013. You can find how it goes in New Year holidays.