Glenn S.’s Answer
Ryan, that is a great question. There are many option.
I chose Product development. This brings products from concept to production.
There is a similar area for sustaining products in production. Redesign or design enhancements.
Test engineering or Reliability Engineers are where products are evaluated and qualified for production.
Manufacturing Engineering where you can set up a factory, factory line, do factory automation, etc.
Supplier Quality Engineer works with suppliers to work with suppliers to deliver parts to specification.
New Product Introduction engineer work between the factory and Product Development to make sure the new products transition to production.
Consultants that work in specific portions of any of the above. They may do the initial design and not work with quualifying for production.
HVAC (Heating Ventilation and Air Conditioning) to spec the ventilation conduits and size of the air handlers for a building.
Technical Sales where you interface with engineers to sell products that meet their needs.
The list can go on forever. I know one ME who used his degree to design a meat smoker and opened a restaurant.