I have a 30 yr old Amana central heater. This morning I set it to go on (auto) and it just hums. The blower won't go on. I unplugged it. What could the problem be?

Sounds like the motor is fried. A non-technical thing to try is:

Turn the breaker off to it.

Manually turn the fan blades (or the "squirrel cage" if you have one).

Now turn the breaker back on.

If the fan comes back on, then the motor is going bad and you've bought yourself some time. If not, time to call the repairman.

It could be a bad start capacitor. Open it up and look at the motor. Give the fan its self a push with your hand, it should turn freely. A capacitor start motor will have a least 4 wires going to it. 2 of them come from the rest of the heater, and 2 of them will run to a round or oval metal can. That is the capacitor. Remove it. It may say something about uf or mf. Take it to an electrical supply and let them match it. Can't promise that is the problem, but very likely if the motor has a capacitor. Not all motors do.

Thank you for the all the information. I appreciate the help.