Get 5-6 copies of the death certificate from the funeral director.

These will be required for several things as you will see below.

Contact Social Security to report the death, and apply for a lump sum death benefit, and a possible increase in Social Security for You. 

You will continue to have access to all jointly-held accounts and safe-deposit boxes. There is usually no need to change those joint accounts immediately. If any accounts are in your spouse's name individually, ask the financial institution for a form affidavit you can use to give you access or close out the account if possible. If you can't get access by affidavit on a form furnished by the financial institution, you'll have to wait until an estate representative is appointed and will likely need to see an attorney for that. 

If your spouse was a veteran, call the VA for burial and other benefits and possible benefits that may be available to you as the surviving spouse. 

Make claims on all life insurance policies and other assets naming you as beneficiary. Roll over IRA's etc., into your name

Contact current and all former employers, unions, and professional groups, notifying then of death and asking about possible death benefits, insurance, pensions etc.

Contact health insurance carrier to inform them of death; try to stay on policy, if you are covered and do not have other insurance.

Cancel credit cards in your spouse's name and notify the company of their death. See if any credit or loan accounts had life insurance.

See the accountant or tax preparer the January after your spouse passes, to complete tax returns.

If any vehicles are in your spouse's name individually, contact DMV for Title and Registration change forms. Contact car and homeowners' insurance carriers regarding the death.

Cancel your spouse's travel reservations, appointments, subscriptions, recurring charges etc. Try to get any deposits back or collect on any relevant insurance. 

Hold onto check registers, cell phone, etc. for possible relevant information. 

Death Certificates (5-6 certified copies)
Social Security Card
Marriage Certificate
Birth Certificate 
Birth Certificate of each child
INsrance Policies
Deeds and Titles to Property
Stock Certificates
Discharge Papers for a Veteran and/or VA Clain Number
Recent Income Taxes, W-2 Forms
Automobile Title & Registration Papers
Loan & Installment Payment Books or Notes

The above is meant for informational purposes only and does not constitute legal advice.