This is not a very difficult question for most larger projects. The problems arise with the smaller projects, such as a fence or a reroof project or a backyard patio or deck.
You can get a lot of different answers for the small projects. Some jurisdictions need the extra revenue and so they require permits for things like fences that are normally exempted. The new International building code has specific exemptions for these types of projects as does the 1997 Uniform Building Code.
All areas of the United States have agreed to eventually adopt the 2000 International Building Code so we will have uniformity in the exemptions across the country.
Fences, not over six feet in height should be exempt from the permit process. You still must meet code requirements but you should not need a permit unless your jurisdiction has enacted a separate ordinance requiring a permit for fencing. If you are being required to permit something that does not seem reasonable, ask to see the legislation or ordinance authorizing the requirement. Local jurisdictions cannot make this demand without supporting authorization in writing.