Public transport in Japan is extremely efficient and safe. It does, however, get very crowded during peak periods.
For peak periods, planes and long-distance trains often get booked up far in advance. The busiest times are the new year, the Golden Week holiday period at the beginning of May, the Obon period in mid-August, and public holidays and school vacations in general. So if you want to travel during these times, make your reservations well in advance.
In addition to the information on this website, the following websites have a number of useful links: