Crocodile (never alligator) and bear dreams have followed me throughout my life. Always grizzly and polar bears, though, for whatever reason, never black bears. Ironically, I've had RL encounters with alligators and black bears. Weird. These dreams are not always scary, but sometime they have been.
Bear in mind that my college training (undergrad) was in bio and zoo(logy), and I've always been interested in the Ursidae and Crocodylidae. The run-ins were pre-puberty. Nothing after that. The alligator experience did kind of border on the mystical. The bear one not so much - just a bear walking through a park that got a bit close.