The thickness of a concrete footing depends on two main factors: the load-bearing value of the soil, and the type of structure. A pole barn, deck and brick house each need different footings. The requirements for these are stated in local building codes.
Load-bearing value is given in pounds per square foot and is a soil's capacity to support a load built on it. Soil with a LBV rating of 1,500, for example, requires a 12-inch footing to support a one-story brick-veneered house. Reed Construction Data is a resource for finding codes specific to each state. The proper footing is crucial to the stability of a building, so its design is best left to qualified architects and engineers.