Japan's high speed trains (bullet trains) are called shinkansen (新幹線) and are operated by Japan Railways (JR).
Running at speeds of up to 186 miles/h, the shinkansen is known for punctuality (most trains depart on time to the second), comfort (relatively silent cars with spacious, always forward facing seats), safety (no fatal accidents in its history) and efficiency.
Most shinkansen trains offer both non-reserved seats and reserved seats in separate cars. Advance seat reservations are required to use a seat in a reserved car.
Train tickets are pretty expensive, like everything in Japan for a foreigner. But travellers can purchase Japan Rail Pass which is valid on almost all trains on the nationwide network of JR, including urban train lines and the shinkansen, as well as on many JR bus lines, the JR Miyajima ferry and the Tokyo Monorail.
Price for 7-days Japan Rail Pass is $350. There are also 14 and 21 day passes ($560 and $700). Only foreigners, who stay in Japan on a temporary visitor visa (and Japanese nationals with permanent residence outside of Japan), are eligible to use a Japan Rail Pass, because it is much cheaper compare to regular tickets. When I was late for the last shinkansen from Osaka to Tokyo, I had to pay around $150 for a single Nozomi train ticket, because my Japan Rail Pass does not work for more fast Nozomi trains, only for slower Hikari train. Travelling time from Osaka to Tokyo (345 miles) is 2 hours and 33 min by Hikari train and 2 hours 18 minutes on Hikari.