Taken straight from the NJ department of Wildlife:
Animals that you do not require any permits to keep
American Anole - Anolis carolinensis
Common iguana - Iguana iguana
Boa constrictor - Constrictor constrictor
Eastern painted turtle - Chrysemys picta picta
Snapping turtle - Chelydra serpentina
Fence lizard - Sceloporus occidentalis & undulatus
Garter snake - Thamnophis spp. (except T. sirtalis tetrataenia)
Tokay gecko - Gekko gecko
Ribbon snake - Thamnophis spp. (except T. sirtalis tetrataenia)Leopard Frog - Rana pipiens
Green frog - Rana clamitans
American toad - Bufo americanus
Fowler's toad - B.w. fowleri
Bullfrog - Rana catesbeiana
Red-spotted newt - Notophthalmus viridescens
Dusky salamander - Desmognathus fuscus
Any invetebrate other than those listed on any relevant Federal or on the State of New Jersey Endangered Species list.
Animals that require permits
Pythons - Family Pythonidae
Rat Snakes - Elaphe spp.
Boas - Family Boidae (other than Boa Constrictor)
King Snakes - Lampropeltis spp.
Racer - Coluber spp.
Ringneck Snakes - Diadophis punctatus
Green Snakes - Opheodrys spp.
Collared Lizard - Crotaphytus collaris
Monitor - Varanus spp.
Skinks - Family Scincidae
Ameiva - Ameiva spp.
Chuckwalla - Sauromalus obesus
Alligator Lizard - Gerrhonotus spp.
Geckos - Family Gekkonidae (other than Tokay Gecko)
Armadillo Lizard - Cordylus cataphractus
African Clawed Frog - Xenopus laevis
Poison Dart Frog - Dendrobates spp.
Argentine Horned Frog - Ceratophrys ornata
Green Treefrog - Hyla cynerea
Cuban Treefrog - Hyla septentrionalis
Red-eyed Treefrog - Agalychnis callidryas
White's Treefrog - Litoria caerulea
Firebelly Toad - Bombina bombina
Firebelly Newt - Cynops pyrrhogaster
Animals considered potentially dangerous
"The Department, at its discretion, may issue a permit for possession of a potentially dangerous species only after a clear showing that the criteria for the possession of such potentially dangerous species have been met.
"Criteria for Possession of Potentially Dangerous Species
The following information is in accordance with N.J.A.C. 7:25-4.8.
(a) "Potentially Dangerous Species" is defined as any exotic mammals, birds, reptiles or amphibians, or nongame species which, in the opinion of the Division, is capable of inflicting serious or fatal injuries or which has the potential to become an agricultural pest, or a menace to the public health, or indigenous wildlife populations, including but not limited to the following:
CLASS/ORDER FAMILY
Primates Cebidae – New World Monkeys
Cercophithecidae – Old World Monkeys
Baboons
Pongidae – Apes
Carnivora Canidae – Nondomestic Dogs
Ursidae – Bears
Felidae – Nondomestic Cats
Saura (Venomous) Helodermatidae – Gila Monsters
Serpentes (Venomous) Elapidae – Coral Snakes & Cobras
Viperidae – Vipers
Crotalidae – Pit Vipers
Crocodilia Alligatoridae – Alligators & Caiman
Crocodylidae – Crocodiles
Gavialidae – Gavials
Psittaciformes Psittaculis spp. – Ring–necked Parakeets
Myiopsitta spp. – Monk (Quaker) Parakeets
Cyanoliseus patagonus – Patagonian Conures
Rodentia Cynomys spp. – Prairie Dogs
Spermophilus spp. – Ground Squirrels
(b) The Department, at its discretion, may issue a permit for possession of a potentially dangerous species only after a clear showing that the criteria for the possession of such potentially dangerous species have been met.
CRITERIA FOR THE POSSESSION OF POTENTIALLY DANGEROUS SPECIES
The following information is in accordance with N.J.A.C. 7:25-4.9.
(a) In addition to the general criteria in section 7:25-4.7, every person applying for a permit to possess potentially dangerous species shall meet each and every of the following criteria to the satisfaction of the Division:
1. Education and Background: Persons wishing to apply for a permit to possess a potentially dangerous species must have extensive experience in maintaining the species desired or related species.
2. Knowledge: Persons wishing to apply for a permit to possess potentially dangerous species must demonstrate a working knowledge and expertise in handling and caring for each of the species desired.
3. Protection of the Public: The housing facilities shall also be constructed to prevent public access to and contact with the animal. The potentially dangerous species shall not be kept as a pet, for hobby purposes or in situations, which, in the judgement of the Department, could adversely affect the health of the animal or which could constitute a hazard to the public.
4. Purpose and Intent: Persons applying to possess potentially dangerous species must submit a written statement of the purpose and intent of keeping the species.
5. Housing and Feeding: Persons applying for a permit to possess a potentially dangerous species must supply a written description of the housing and caging facilities for the species required. A summary must be submitted of a continuous source of food for the specific diet of the animals. Division personnel may inspect the completed facilities to determine if the facilities are suitable for the animal. Facilities must be constructed to prevent the possible escape of the animal.
6. Other Restrictions: Under no circumstances shall a person issued a pet shop or animal dealer permit possess any potentially dangerous species on the commercial premises, except in emergencies and for a limited period of time as stipulated by the Department in writing and subsequently agreed to by the animal dealer or pet shop owner, who shall assume full responsibility for the safety and welfare of both the animal and the public during its temporary storage. A potentially dangerous animal already on display at the premises of a pet shop or animal dealer and already under a permit for such display as of January 17, 1995 may remain so displayed under the terms and conditions of that permit for the lifetime of that animal."
I've only gotten PA and MD done so far, but I would be more then happy to repost the information as I acquire it. 