Alligators are protected by both Florida and federal law because of their similarity to the American Crocodile. The southern tip of Florida, from about Ft. Myers on the Gulf Coast to Coral Gables just south of Miami, is the northern limit of the American Crocodile's range. The greatest concentration of American Crocodiles is in the cooling canals of the Turkey Point nuclear power plant south of Miami, but they are routinely seen (every day) in some places in Everglades National Park. In the marina area of Flamingo in Everglades NP, alligators and crocodiles are often seen swimming alongside each other, but they do not breed with each other. Crocodiles have been found on Sanibel Island in the Ft. Myers area and several times on the campus of the University of Miami in Coral Gables.
Alligators are not just protected from killing, it is also illegal to feed them, harass them, or basically disturb them in any way. Theoretically, if you approach an alligator and they go into the water in response, you could be charged. That's not likely to happen, but it could.
Very limited "harvesting" is permitted, by lottery-driven permit only, during a very short period most years. The number of permits is limited, and in the last few years not all of the permits have been taken -- probably because it's not profitable due to competition with commercial operations.
Florida has a number of licensed alligator farms where alligators are raised for their meat and hides, but the taking of wild alligators is a crime except by permit during the annual "harvests.," Enforcement is aggressive by both state and federal authorities.