The only reason I would not submit a FAFSA is if my parents were going to pay for my medical school. And I mean the whole shabang: tuition, room and board, transportation, etc..
FAFSA is required by all schools if you are going to seek institutional aid. This aid is usually given to the needest students. Thus, if you're parents are well off and will contribute to school, you probably won't get aid.
Also, you have to complete a FAFSA to "apply" for Stafford loans, again if your parents are paying for school, there is no need.
I have friends whose parents are either paying for their tuition or their room and board, but they still completed a FAFSA since they had to take out loans for the portion that wasn't covered. I, myself, am fortunate that my parents will be covering everything except my tuition and I completed the FAFSA because I need to obviously borrow ~30K.