My question is, should I replace them?

[Ellisy]

I have a 40 year old American Standard Air natural gas furnace and a 20 year old air conditioning unit and coil (no idea what brand/manufacturer).

They both still run, but i have unreasonably high heating/cooling bills.
And if replacing is the best option, what are some system recommendations?

[juster]

If your intent is to save energy then the answer is yes. Minimum standards have greatly improved over the last 30 years and by simply replacing with new of a minimum standard you will be saving energy. If you were to choose high efficiency equipment you would save even more energy.