How old is your furnace?
IF it's an older furnace , it is controlled by a fan/limit switch.
The switch controlls the fan motor by the amount of heat that is in the heat exchanger box. These swiths do go bad. It is normally a silver box mounted above your burners. Tap on this box and see if the blower shuts off. If it does ,the switch is bad. And also make sure the fan switch on your thermostat is in the auto position. To check thermostat to see if thats the problem, turn power off the furnace with the breaker and remove wire off of G on your low voltage terminal strip and turn power back on. If fan is not running, its in the thermostat.
Don Cromer, December 2004