STATE LAW
The U.S. Constitutions have given each individual state the right to dictate the laws that will be in effect regarding the manufacture of home brewed beer or other alcoholic substances. Do not assume what is legal in one state will be legal in the next state. You don't want to see a new hobby of yours turn into a nightmare of legal issues.
Alabama, for one, clearly states that it is illegal in all counties to have any equipment or apparatus used to manufacture any kind of alcoholic beverages. It's also illegal there to have any illegally manufactured beverages brought into the state or transported inside the state.
Most of the states in the United States, however, do permit home brewing. There are some restrictions to the amounts of beer and the age of the person brewing. Most of these laws allow no more than 100 gallons of home brew per person per household and the person must be over the age of 21.
The maximum they can brew per year is 200 gallons. People that brew their own beers are restricted from selling it because the federal government taxes alcohol through excise taxes. Most Western countries have the same home brewing laws.
In Michigan, for instance, it's perfectly legal to brew your beer if you are over 21 years of age but only up to 100 gallons. You can give your home brew to other people, but you cannot sell it. The 100 gallons, incidentally, can be broken down into 20 5-gallon batches of brew. Many home brewers like making smaller amounts at one time so they can experiment with different flavors, colors and varieties.
Kentucky, on the other hand, prohibits anyone from having in their possession any apparatus used in the manufacture of any alcoholic beverage including home brew. While they are more concerned with illegal distilling, their laws can also be extended to the home brewing of beer.