Rental Insurance
It is important to determine whether you are already insured!
It is not uncommon for your parents'/guardian homeowner's policy to include coverage on personal property away from home. Usually a percentage of the total coverage would apply to your belongings at school. Call your insurance company to check on what would be covered away from home in case of flood, fire, or theft, before you move into your apartment.
If you decide that you actually need a renter's policy of your own, you may shop around to ascertain the best deal.
For additional information visit the Brown Office of Insurance and Risk at:
http://www.brown.edu/Administration/Office_of_Insurance_and_Risk/students/property.html