You need to look it up state by state, try to find the the Wildlife Division Resources website for each state you might me interested in.

GA is pretty strict

You can't own

Mammals:

Armadillo -Bats, all species - Black Bear - Bobcat - Chipmunk - Cottontail Rabbit - Coyote - Cougar - Flying Squirrel - Fox Squirrel - Gray Fox - Gray Squirrel - Groundhog - Marsh Rabbit - Mink - Mole - Muskrat - Opossum - Pocket Gopher - Raccoon - Red Fox - River Otter - Skunk - Swamp Rabbit - Weasel - White-tailed Deer.

Reptiles and Amphibians:

Alligator - Alligator Snapping Turtle - Black Racer - Bog Turtle - Box Turtle -(Eastern, Florida, Gulf Coast, Three-toed) - Brown Snake - Coachwhip - Corn Snake - Crayfish Snake (Glossy, Striped) - Crowned Snake (Southeastern, Central Florida) - Diamondback Terrapin - Earth Snake (Rough, Smooth) - Fence Lizard - Flatwoods Salamander - Florida Worm Lizard - Garter Snake -Georgia Blind Salamander - Glass Lizard (Eastern, Island, Mimic, Slender) - Gopher Tortoise - Green Anole - Green Salamander - Hellbender - Hognose Snake (Eastern, Southern) - Indigo Snake - Kingsnake (Black, Eastern, Mole, Scarlet) - Map Turtle (Alabama, Barbour's, Common) - Milksnake - Mud Snake - One-toed Amphiuma - Pigeon Mountain Salamander - Pine Snake (Florida, Northern) - Pine Woods Snake - Queen Snake - Rainbow Snake - Rat Snake (Black, Gray, Yellow) - Redbellied Snake - Ribbon Snake - Ringneck Snake - Rough Green Snake - Scarlet Snake - Sea Turtle (Green, Hawksbill, Leatherback, Loggerhead, Ridley) - Six-lined Racerunner - Skink (Broadhead, Coal, Five-lined, Southeastern Five-lined, Ground, Mole) - Spotted Turtle - Striped Newt - Water Snake (Banded, Brown, Florida Green, Northern, Redbelly) - Worm Snake