Yes, every individual will need their own NIF.
If you are a married couple, you will both need separate NIF numbers.
You will need your unique NIF number to sign up for health insurance, bank account (even if it’s joint), a cell phone contract, etc.
See a few more examples here of what you can do with your own NIF in Portugal.
Children also need their own NIF in order to enroll in a school in Portugal.