Why would the fan motor on Honda Accord run by itself?

Many cars with electrically operated cooling fans will continue to run if the engine coolant is above the temperature sensors trigger level (usually somewhere between 80 to 98 degrees Celsius) even after the engine is stopped and the ignition switched off.

These types of fans should switch off once the coolant in the radiator has dropped to the designated temperature (usually around 2 to 3 minutes). If the fan doesn't switch off at all however - there may very well be a fault in the temperature sensor or the wiring to the fan and this should be checked out by a competent mechanic/auto-electrician.