Bryant furnace around 25 years old. Working fine till the other day. Heater comes on but the blower continues to run when the heat goes off. Turn off furnace @ thermostat & blower keeps running. Need to go down & hit off the main switch by the heater. Turn the heater back on & it seems to run OK for a few hours & than the same thing happens.

This problem sounds to me like you have a relay that the points are sticking in, If this is the model furnace that I think it is you have a metal box with a PC board in it with the relays on the PC board. To get to it take off the upper door, on the left side of the heater about 48 inches high is the metal box, it has two screws holding a cover on it. Take the cover off and you will see two relays about 1 1/2 inch X 2inches they are a brown color. The next time your furnace will not turn off use something like a wooden handle of a hammer and tap lightly on each of the relays and notice if one of them makes the motor stop running. If so replace that relay, they are what is called a plug-in relay so pur straight out on it and it will slip out of the socket. Some relays had a wire type spring that is around the relay to keep it from popping out while in use, so you may have to move this spring. Good luck. Remember this is for just the one model furnace that I think you may be describing that is about 25 years old.