Depends on the school
The newer schools will have little to no scholarships since they have been focused on starting the school (and recruiting staff) and likely there is little dedicated fundings for scholarships
The older establish schools (DMU, PCOM, KCOM, etc) have a large alumni base and have had time to establish various scholarships (ie Class of 1927 scholarship, Class of 1950 scholarship, the Dr John Doe Memorial Surgical Scholarship for students interested in surgery, the Dr Jane Doe Emergency Medicine Scholarship for excellence in emergency medicine rotation, etc). Usually with a large (and older) alumni base, there is time for its alumni to make money, reflect on life, and donate to the school (either into the unrestricted fund, or establish a trust/endowment in memory of someone they love, or give at class reunion to establish a class scholarships).
When I was at PCOM, I received the Board of Trustees Scholarships, some class memorial scholarships, and even some scholarships sponsored by companies (PCOM selected who received them) such as Office Max, Lowes, Home Depot, etc.,
This is one of those topics that many people on SDN don't talk about (in regards to new school vs old school) ... now $5k/year or $10k/year may not sound like a lot (compare to tuition), but multiply that over 4 years, and you are talking about a $20k-$40k in scholarships (and if you convert that into loans at current interest rates, you are saving a lot of money throughout your lifetime by NOT having to borrow that additional amount)
These scholarships (or at least the ones I received) were a mixed of pure financial need and some were academics.
*I wonder if schools count students receiving the HPSP scholarships when they report how much aid students receive (and why the percentage is so high at some school)