Most animals generally won't mess with crocodiles or alligators. There's an infamous photo of a Burmese python that died while trying to eat an alligator in the Everglades (see link), although the python was likely a released pet and would not have encountered the gator under normal conditions. Hippos can also pose a threat to crocodiles, though both tend to leave each other alone.
Edit: Agreed with Sinister Serpent, yeah. I figured humans were a given, but yes. Human are the #1 threat to alligators, crocodiles, gavials, caimans, etc. etc.
Once they are full grown there is not much that could kill and eat an alligator or crocodile. But while young, the first several years at least, they are vulnerable to pretty much all predatory animals they share habitat with, including larger snakes and alligators.
It's actually estimated that about 50% of young alligators are eaten by larger ones, though environmental factors play a big role in this behavior. This high predation rate is also likely the reason that young alligators are guarded by their mothers for up to two years.
For adult alligators there are very few natural enemies, but crocodiles in Africa have been known to scuffle with large predators such as lions and hippo. The first usually in fights over other prey items rather than actual crocodile/lion predation, and the second usually for territorial reasons.
Young are eaten by a verity of predators like cats, raccoons, otters, herons, snakes, fish, snapping turtles, and other crocodilans. Even subadult and smaller species can be preyed upon by large cats, eagles , hawks and large boid snakes.