According to the Federal Emergency Management Agency (FEMA) you should have the following documents available in case of an emergency:

Vital records. A wide variety of documents fits under this category, and you should make sure to have multiple copies of each of them: birth certificates, Social Security cards, adoption papers, passports, driver's licenses, state IDs, permanent resident cards and naturalization papers. Also include marriage certificates, divorce decrees, child custody papers, military IDs and military discharge forms.
Don't forget about family pets! You should make sure to have current photos, their ID chip numbers, as well as vaccination and medical records.
Property records. These include real estate deeds, mortgage documents, rental agreements, and vehicle and boat registrations. Take the time to create a household inventory list, and try to take and store photos of every item.
Insurance policies. Even if you have online accounts, print out policy information for health, life, auto, and homeowners or renters insurance. Don't forget to include any information on specialty insurance coverage, such as earthquake, flood or disability. Make sure you have contact numbers handy for each insurance company.
Medical documents. Health insurance ID cards, medical records, immunization records, medication lists, physician names and contact details should be copied and filed for each family member. Try to get a hold of dental records, too.
Estate planning documents. These include power of attorney documents, attorney names and contact details, trusts, wills and funeral instructions.
Financial documents. Save checking, savings and credit card account numbers. Include investment documents, retirement account and brokerage information, and stock and bond certificates. Also, having the first two pages of your federal and state tax returns for at least the previous year is a good idea.