One of my favorite records are Homestead Exemptions. I've used these records to help better understand the lives of my ancestors and fill in the blanks between census years. So far I've used them to research my Georgia ancestors. Georgia's records began in 1852 but, as these were state created laws, they began at different times in different states. According to the Georgia Archive, "the basic purpose of this exemption is to make a certain amount of person's property untaxable."
Given the purpose of the records, you might be able to guess what kind of information is included: the person who is seeking tax protection and details on the property needing protection. These records will list the head of the household and in some list his family members. Often, every member of the household will be listed by name; it's like a mini census! Then there is a list of property, such as acres of land, livestock, furniture, and seemingly random items such as sewing machines and guns. Sometimes you'll luck up and the record will include a plat map.
For example, you can see the Homestead Exemption application for my Great-Great-Great Grandfather, William W Sprouse. This record was filed in 1889 - hey, look at that! It's like a stand-in for the destroyed 1890 census. It lists William, wife Nancy, and children Tully, Walter, Nina, Miller and Bernie. This was exciting for me, in part because my Great-Great Grandmother, Nina Sprouse, never appeared on a census record with her parents. The record also lists the family's property and it's value. It's interesting to see the price of things in 1889.
Finding these records is always exciting for me, even though they tend to indicate that my ancestors were struggling financially. They are a bit of a gold mine and may help you learn something new about your ancestors.