Sports Car Club of America
The SCCA could be considered the 'grass-roots' level of auto racing in the United States. It runs many different programs for both amateur and professional racers.
The club racing program[1] (http://www.scca.org/amateur/club_racing/index.html) is what most people think of when they think auto racing... cars on a purpose-built racetrack. The big difference is that the drivers aren't paid (they do it for fun), and almost any car can be used as a race car, even cars that are stock (except for the addition of a roll cage, fire extinguisher and window net).
The Solo program[2] (http://www.scca.org/amateur/solo2/index.html) is what many people would call autocross. One car at a time, running a course laid out with orange cones in a big parking lot. Truly a case of 'run what you brung', the only race-centric requirement is a helmet.
Road Rallies[3] (http://www.scca.org/amateur/roadrally/index.html) are run on open, public roads. These are not races in the sense of speed (obviously, speed limits are to be obeyed), but of precision and navigation. The object is to drive on time, arriving at checkpoints with the proper amount of elapsed time from the previous checkpoint. Trick is, you don't know where the checkpoints are.
The SCCA ProRally is a national performance Rally series similar to the World Rally Championship.
The SCCA also has many professional series[4] (http://www.sccapro.com/index.html) like the Trans-Am series.