The USA does ban some species for possession.
link malfunction, you'll ave to find it with key words
http://usasearch.gov/
Title 50: Wildlife and Fisheries
PART 16—INJURIOUS WILDLIFE
Subpart B—Importation or Shipment of Injurious Wildlife
You can not legally own any of these animals without a federal permit and none are given for pet Sad
Any species of so-called “flying fox” or fruit bat of the genus Pteropus ;
any species of mongoose or meerkat of the genera Atilax, Cynictis, Helogale, Herpestes, Ichneumia, Mungos, and Suricata ;
any species of European rabbit of the genus Oryctolagus ;
any species of Indian wild dog, red dog, or dhole of the genus Cuon ;
any species of multimammate rat or mouse of the genus Mastomys ;
any raccoon dog, Nyctereutes procyonoides ; and
any brushtail possum, Trichosurus vulpecula :
Birds
the species of so-called “pink starling” or “rosy pastor” Sturnus roseus ; the species of dioch (including the subspecies black-fronted, red-billed, or Sudan dioch) Quelea quelea ;
any species of Java sparrow, Padda oryzivora ;
the species of red-whiskered bul-bul, Pycnonotus jocosus :
The rest is fish and mollusks.
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Here's the text
§ 16.11 Importation of live wild mammals.
(a) The importation, transportation, or acquisition is prohibited of live specimens of: (1) Any species of so-called “flying fox” or fruit bat of the genus Pteropus ; (2) any species of mongoose or meerkat of the genera Atilax, Cynictis, Helogale, Herpestes, Ichneumia, Mungos, and Suricata ; (3) any species of European rabbit of the genus Oryctolagus ; (4) any species of Indian wild dog, red dog, or dhole of the genus Cuon ; (5) any species of multimammate rat or mouse of the genus Mastomys ; (6) any raccoon dog, Nyctereutes procyonoides ; and (7) any brushtail possum, Trichosurus vulpecula : Provided, that the Director shall issue permits authorizing the importation, transportation, and possession of such mammals under the terms and conditions set forth in §16.22.
(b) Upon the filing of a written declaration with the District Director of Customs at the port of entry as required under §14.61, all other species of live wild mammals may be imported, transported, and possessed in captivity, without a permit, for scientific, medical, educational, exhibition, or propagating purposes, but no such live wild mammals or any progeny thereof may be released into the wild except by the State wildlife conservation agency having jurisdiction over the area of release or by persons having prior written permission for release from such agency: Provided, That the provisions of this paragraph shall not apply to live game mammals from Mexico, the importation of which is governed by regulations under part 14 of this chapter.
[39 FR 1169, Jan. 4, 1974, as amended at 47 FR 56362, Dec. 16, 1982; 67 FR 39868, June 11, 2002]
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Since specific genra of mongoose are listed those not listed are allowed so this is why you see certain species sometimes like cusimanse and pygmy.
Genus Bdeogale (mongooses)
Genus Crossarchus (cusimanses)
Genus Dologale (Pousargues's mongoose)
Genus Galerella (slender mongooses)
Genus Liberiictis (Liberian mongoose)
Genus Paracynictis (Selous's mongoose)
Genus Rhynchogale (Meller's mongoose)
I'm sure they only enforce the rabbits and mice on the non domestic species. Rabbits have been stopped at the airport or boarder when shipping if the scientific name is written but if domestic rabbit is written they have no problems. Obviously same species but if a wild one you couldn't write domestic rabbit and would have to write European rabbit or the species name and then it wouldn't be allowed.
