What happens when a married person dies and leaves no will?

Generally, when a married person dies intestate (without a will) any interest in property held with the spouse as joint tenants with the right of survivorship, or tenants by the entirety, automatically passes to the spouse. Any individually owned property passes according to the laws of intestacy. Those general rules govern non-community property. Property is distributed differently in community property states. See the related question below for a link to state by state intestacy laws.