Although adult alligators are at the top of the food chain and have no predators their young do. The young juvenile alligators are vulnerable to big fish, birds, mammals, and even larger alligators. This is why the mother is so protective for the first year or two. After this they are fine and do not have to worry about predation anymore.
Alligators are usually not offensive to people unless provoked. The only time that people really have a problem with them is when the dry season gets to dry and the gators start looking for bodies of water. They sometimes end up in peoples swimming pools! This is when people usually get to close to them and provoke an attack. Most of the time they will just leave or the animal control agencies will come and capture them and take them back to the wilderness. Although there have been alligator attacks on man, it is not a common thing. They would rather not be near you if they did not have to be. Feeding alligators is what makes them dangerous because then they associate you with food. This makes them way to comfortable with people and causes problems.