I have a Goodman GMP125-4 A/C that is about 11 years old. Gas heat, electric cool. I have lived here for a little more than two years, and within the past 3 months, I've noticed that the fan comes on a lot. A lot means it will come on for 5 or so minutes, shut off for 30 seconds to a minute, then start over. It is just the fan, not hot air, not cold air. The thermostat is set to Heat and Fan is set to Auto. About 3 weeks ago, I installed a programmable thermostat and still no change. Why does the fan come on by itself normally? Also, any suggestions to correct this, if it is a problem at all?
Thanks for any help you can provide.

Usually there is a cause for this.
It could be a defective relay
Defective fan limit control set at a bad balance point.
If the unit has a circuit board that controls the blower it could be bad also.

It would be best to hook up a meter and when it happens trace the blower circuit down to find the defective part cause that is the only way to find the problem without just replacing many expensive parts.