Depends on what type of train I guess. Probably no bullet train (shinkansen) has even been more than 59 seconds late (under normal circumstances that is). Naturally any type of bad weather like blizzards, typhoons or earthquakes will cause delays but most likely due to a complete cancellation of service.
Local trains are more prone to delays, for example the Yamanote line in Tokyo being the most notorious due to ahem, being the preferred line used by Tokyoites to say bye-bye to this world.
For local city train lines a delay of more than 5 minutes will result in the driver profusely apologizing on and on, and the line to start issuing "certificates" that people can get to show their employers blaming the lateness on the train line.
Local trains are more prone to delays, for example the Yamanote line in Tokyo being the most notorious due to ahem, being the preferred line used by Tokyoites to say bye-bye to this world.
For local city train lines a delay of more than 5 minutes will result in the driver profusely apologizing on and on, and the line to start issuing "certificates" that people can get to show their employers blaming the lateness on the train line.