Make sure to have copies of each family member's Social Security card, birth certificate, and passport, and keep them stored in an easy-to-access location. You should grab these as well as the originals during an evacuation.
For documents that are equally important but not emergency necessities — insurances, medical records, financial information, and wills — scan them onto your computer and upload to Google Drive, iCloud, or another online server. This way you will have access to them should they be destroyed during the storm.
Source: Flickr user abstractlight