Tenants may want to consider investing in renters' insurance, something many do without but which can be important.

Weather and environmental effects in 2011 brought down trees that did significant damage in New York City, according to the New York Times. While damage from an earthquake like the one experienced last August may not be covered under renters' insurance, more common occurrences like wind, lightning and rain generally are included in basic policies.

A landlord's insurance policy typically protects the residential property itself, but may not help a tenant whose belongings are damaged. Only minimal protection is extended when tenants sign their property lease documents, in most cases.

"As a renter, if your personal property is damaged, you’d have to have a renter’s policy to get coverage," associate insurance examiner John Capuano told the news source. "The landlord’s policy is not going to cover your damages."

Renters' insurance, on the other hand, can provide coverage in case of theft or vandalism, and losses to smoke or fire. It may also provide for living expenses in the event that a renter is forced out of his or her apartment because a fire makes it unusable as a residence.