One of the most popular times to visit Japan is during the Cherry blossom at the end of march.
More pictures here.
Sakura (Cherry blossom) season in Japan is one of the best times to enjoy the gifts Japanese culture has to offer. People in Japan love this time because it is an excuse to eat and drink under the blossoming trees all day! One of the most beautiful places in Tokyo to watch Sakura is the Imperial Palace gardens. Here is a list of popular spots around Japan.
The Cherry blossom is predicted to occur on the 27th of march in Tokyo and in Kyoto on the following day. On this page you will find more cities and dates for the blossom.
The cherry blossom season is relatively short. Full bloom (mankai) is usually reached within about one week after the opening of the first blossoms (kaika). Another week later, the blooming peak is over and the blossoms are falling from the trees. Strong wind and rain can cut the blooming season even shorter.