Should I close off the registers (aka diffusers, vents, grills, etc.) in unused areas/rooms in my home?

You should not fully close too many registers in unused areas because this can cause comfort issues and reduced system efficiency. By closing registers you are restricting airflow, causing higher system static pressure. The system in your home was designed to run with all of your registers open.
The only time you should be closing your registers is if one area gets to be way to hot or cold compared to the rest of your home!