Here is my lists of rare mammals (always my focus)
First my top 30 in no particular order:
1.) (Saiga tatarica) saiga (San Diego Zoo & WAP)
2.) (Nilgiritragus hylocrius) Nilgiri Tahr (San Diego Zoo)
3.) (Ourebia ourebi) Oribi (San Diego WAP)
4.) (Pelea capreolus) Grey Rhebok (Private Holder in TX)
5.) (Cephalophus jentinki) Jentink's Duiker (Gladys Porter’s Zoo)
6.) (Cephalophus zebra) Zebra Duiker (LA Zoo)
7.) (Bubalus quarlesi) Mountain Anoa (Krefeld Zoo)
8.) (Tetracerus quadricornis) Four-horned Antelope (Delhi Zoo)
9.) (Mazama bricenii) Merida Brocket Deer (Parque Jaime Duque in Bogota)
10.) (Dicerorhinus sumatrensis) Sumatran Rhinoceros (LA, Bronx, San Diego, Cincinatti Zoos)
11.) (Dugong dugon) dugong (Sea World, Gold Coast, Australia)
12.) (Tapirus pinchaque) Mountain Tapir (Cali, San Diego Zoo, LA)
13.) (Hydrurga leptonyx) leopard seal (Taronga Zoo)
14.) (Mirounga angustirostris) northern elephant seal (Pacific Marine Mammal Center)
15.) (Leopardus pajeros) Pampas Cat (Cincinatti Zoo)
16.) (Eschrichtius robustus) gray whale (San Diego Sea World)
17.) (Inia geoffrensis) Amazon river dolphin (Duisburg Zoo)
18.) (Nasalis larvatus) proboscis monkey (Bronx Zoo)
19.) (Ictonyx striatus) Zorilla (Paradise Wildlife Park in Broxbourne UK)
20.) (Ornithorhynchus anatinus) Duck-billed platypus (Healesville Sanctuary, Taronga Zoo, Sydney Aquarium)
21.) (Chironectes minimus) Yapok (Dallas World Aquarium)
22.) (Dendrolagus lumholtzi) Lumholtz’s Tree-kangaroo (David Fleay WP)
23.) (Spilocuscus maculates) Common Spotted cuscus (San Diego Zoo)
24.) (Macrotis lagotis) Bilby (David Fleay WP, Taronga Zoo)
25.) (Fossa fossana) Malagasy or striped civet (Capital of Texas Zoo)
26.) (Prionodon linsang) Banded Linsang (San Diego WAP)
27.) (Cephalopachus bancanus) Western Tarsier (Cleveland Zoo)
28.) (Oreonax flavicauda) Yellow-tailed Woolly Monkey (Cali Zoo)
29.) (Priodontes maximus) giant armadillo (Zoologico los ocarros, Columbia)
30.) (Manis tricuspis) Tree Pangolin (San Diego Zoo)
Now the full list: I went through my total species list and tried to only include animals that are kept in a handful of places (or not at all). Unfortunately I can't double check rarity through ISIS, and had to just rely on memory or zootierliste. I didn't feel like writing where I saw each one, but if anyone has any specific questions feel free to ask!!
1.) (Ornithorhynchus anatinus) Duck-billed platypus
2.) (Monodelphis brevicaudata) red-legged short-tailed opossum
3.) (Philander opossum) Four-eyed opossum
4.) (Chironectes minimus) Yapok
5.) (Phascogale calura) Red-tailed Phascogale
6.) (Antechinus agilis) Agile Antechinus
7.) (Sminthopsis douglasi) Julia Creek Dunnart
8.) (Dasycercus byrnei) Kowari
9.) (Dasyurus hallucatus) Northern Quoll
10.) (Dasyurus viverrinus) Eastern quoll
11.) (Dasyurus maculates) Tiger quoll
12.) (Sarcophilus harrisii) Tasmanian devil
13.) (Macrotis lagotis) Bilby
14.) (Parameles gunnii) Eastern Barred Bandicoot
15.) (Trichosurus caninus) Mountain Brushtail Possum
16.) (Spilocuscus maculates) Common Spotted cuscus
17.) (Bettongia tropica) Northern Bettong
18.) (Bettongia gaimardi) Tasmanian, Eastern Bettong
19.) (Aeprprymnus rufescens) Rufous Bettong
20.) (Dendrolagus lumholtzi) Lumholtz’s Tree-kangaroo
21.) (Petrogale persephone) Proserpine Rock-wallaby
22.) (Petrogale penicillata) Brush-tailed Rock-wallaby
23.) (Petrogale lateralis) Black-footed Rock-wallaby
24.) (Onychogalea fraenata) Brindled nail-tailed Wallaby
25.) (Macropus dorsalis) Black-striped Wallaby
26.) (Cercartetus nanus) Eastern Pygmy-possum
27.) (Burramys parvus) Mountain Pygym-possum
28.) (Petaurus australis) Yellow-bellied Glider
29.) (Petaurus gracilis ) Mahogany Glider
30.) (Manis pentadactyla) Chinese Pangolin
31.) (Manis tricuspis) Tree Pangolin
32.) (Elephantulus rufescens) Rufous Elephant-shrew
33.) (Rhynchocyon cirnei) Checkered Elephant Shrew
34.) (Tupaia minor) pygmy tree shrew
35.) (Tupaia tana) large tree shrew
36.) (Tamandua mexicana) northern tamandua
37.) (Bradypus variegatus) brown-throated three-toed sloth
38.) (Priodontes maximus) giant armadillo
39.) (Neomys fodiens) Eurasian Water Shrew
40.) (Suncus murinus) Asian House Shrew
41.) (Atelerix frontalis) Southern African Hedgehog
42.) (Tenrec ecaudatus) tailless tenrec
43.) (Cynopterus brachyotis) Lesser dog-faced fruit bat
44.) (Pteropus conspicillatus) Spectacled flying fox
45.) (Pteropus poliocephalus) Grey-headed flying fox
46.) (Pteropus pumilus) Little Golden-mantled Flying Fox
47.) (Pteropus scapulatus) Little red flying fox
48.) (Macroderma gigas) Ghost bat
49.) (Noctilio leporinus) Greater bulldog bat
50.) (Cephalopachus bancanus) Western Tarsier
51.) (Nycticebus bengalensis) Bengal slow loris
52.) (Cheirogaleus medius) fat-tailed dwarf lemur
53.) (Microcebus lehilahytsara) Goodman's mouse lemur
54.) (Mirza coquereli) Coquerel's giant mouse lemur
55.) (Eulemur cincereiceps) gray-headed lemur
56.) (Hapalemur griseus) Gray Bamboo Lemur
57.) (Hapalemur occidentalis) Western Lesser Bamboo Lemur
58.) (Cebus albifrons) white-fronted capuchin (Omaha, Bogota)
59.) (Chiropotes chiropotes) Red-backed bearded saki
60.) (Chiropotes utahicki) Uta Hick's bearded saki
61.) (Pithecia monachus) Monk saki
62.) (Alouatta Pigra) Guatemalan Black Howler Monkey
63.) (Aotus miconax) Peruvian night monkey
64.) (Aotus nigriceps) Black-headed night monkey
65.) (Oreonax flavicauda) Yellow-tailed Woolly Monkey
66.) (Saguinus leucopus) White-footed tamarin
67.) (Callicebus moloch) Dusky titi monkey
68.) (Callicebus oenanthe) San Martin Titi Monkey
69.) (Cacajao calvus) Red Uakari
70.) (Cercopithecus campbelli) Campbell's guenon
71.) (Cercopithecus pogonias) crowned guenon
72.) (Papio ursinus) Chacma baboon
73.) (Cercocebus agilis) agile mangabey
74.) (Macaca arctoides) stump-tailed macaque
75.) (Macaca hecki) Heck's macaque
76.) (Macaca sinica) toque macaque
77.) (Nasalis larvatus) proboscis monkey
78.) (Presbytis comata) Javan surili
79.) (Presbytis melalophos) banded surili
80.) (Pygathrix nemaeus) red-shanked douc langur
81.) (Hoolock hoolock) western hoolock gibbon
82.) (Nomascus siki) southern white-cheeked gibbon
83.) (Vulpes chama) Cape fox
84.) (Urocyon littoralis) island fox
85.) (Cerdocyon thous) Crab-eating fox
86.) (Lycalopex culpaeus) Colpeo fox
87.) (Lycalopex sechurae) Sechura fox
88.) (Procyon cancrivorus) Crab-eating Raccoon
89.) (Bassariscus sumichrasti) Central American Cacomistle
90.) (Mustela nigripes) Black-footed Ferret
91.) (Galictis cuja) Lesser grison
92.) (Galictis vittata) Greater grison
93.) (Ictonyx striatus) Zorilla
94.) (Poecilictus libyca) Libyan striped weasel
95.) (Melogale moschata) Chinese ferret-badger
96.) (Conepatus leuconotus) American hog-nosed skunk
97.) (Mephitis macroura) hooded skunk
98.) (Aonyx capensis) African clawless otter
99.) (Lontra feline) Marine otter
100.) (Lontra longicaudis) Neotropical otter
101.) (Fossa fossana) Malagasy or striped civet
102.) (Nandinia binotata) African palm civet
103.) (Prionodon linsang) Banded Linsang
104.) (Arctogalidia trivirgata) Small-toothed Palm Civet
105.) (Chrotogale owstoni) Owston's palm civet
106.) (Hemigalus derbyanus) banded palm civet
107.) (Paguma larvata) Masked Palm Civet
108.) (Viverra tangalunga) Malayan Civet
109.) (Genetta felina) feline genet
110.) (Genetta thierryi) Haussa Genet
111.) (Galerella sanguinea) Slender Mongoose
112.) (Ichneumia albicauda) White-tailed Mongoose
113.) (Leopardus pajeros) Pampas Cat
114.) (Eschrichtius robustus) gray whale
115.) (Phocoena phocoena) harbour porpoise
116.) (Inia geoffrensis) Amazon river dolphin
117.) (Sousa chinensis) Indo-Pacific humpback dolphin
118.) (Stenella frontalis) Atlantic Spotted Dolphin
119.) (Stenella longirostris) Spinner Dolphin
120.) (Steno bredanensis) Rough-toothed Dolphin
121.) (Arctocephalus townsendi) Guadalupe fur seal
122.) (Arctocephalus tropicalis) subantarctic fur seal
123.) (Hydrurga leptonyx) leopard seal
124.) (Monachus schauinslandi) Hawaiian monk seal
125.) (Mirounga angustirostris) northern elephant seal
126.) (Pusa sibirica) Baikal seal
127.) (Dendrohyrax arboreus) Southern Tree Hyrax
128.) (Dugong dugon) dugong
129.) (Tapirus pinchaque) Mountain Tapir
130.) (Dicerorhinus sumatrensis) Sumatran Rhinoceros
131.) (Potamochoerus larvatus) bushpig
132.) (Tragulus kanchil) Lesser Malay chevrotain
133.) (Tragulus nigricans) Balabac chevrotain
134.) (Cervus bactrianus) Bactrian Deer
135.) (Hyelaphus calamianensis) Calamian Deer
136.) (Hyelaphus kuhlii) Bawean deer
137.) (Mazama bricenii) Merida Brocket Deer
138.) (Mazama gouazoubira) Gray Brocket Deer
139.) (Mazama temama) Central American Red Brocket
140.) (Ozotoceros bezoarticus) Pampas deer
141.) (Tragelaphus Scriptus) Bushbuck
142.) (Tetracerus quadricornis) Four-horned Antelope
143.) (Bubalus quarlesi) Mountain Anoa
144.) (Cephalophus dorsalis) Bay Duiker
145.) (Cephalophus jentinki) Jentink's Duiker
146.) (Cephalophus zebra) Zebra Duiker
147.) (Philantomba maxwellii) Maxwell's Duiker
148.) (Sylvicapra grimmia) Common Duiker
149.) (Kobus kob) Kob
150.) (Pelea capreolus) Grey Rhebok
151.) (Redunca fulvorufula) Mountain Reedbuck
152.) (Alcelaphus buselaphus) Jackson's hartebeest
153.) (Alcelaphus caama) Red Hartebeest
154.) (Madoqua guentheri) Günther's Dik-dik
155.) (Neotragus moschatus) Suni
156.) (Ourebia ourebi) Oribi
157.) (Eudorcas rufifrons) Red-fronted gazelle
158.) (Saiga tatarica) saiga
159.) (Nilgiritragus hylocrius) Nilgiri Tahr
160.) (Naemorhedus goral) Himalayan Goral
161.) (Rupicapra pyrenaica) Pyrenean chamois
162.) (Ovis nivicola) snow sheep
163.) (Acomys spec. nov.) Mount Kulal spiny mouse
164.) (Apodemus uralensis) Pygmy field mouse
165.) (Beamys hindei) Long-tailed pouched rat
166.) (Dryomys nitedula) Forest dormouse
167.) (Eliurus grandidieri) Grandidier’s Tufted-tailed Rat
168.) (Grammomys caniceps) Gray-headed thicket rat
169.) (Graphiurus parvus) Savanna dormouse
170.) (Lemniscomys rosalia) Single-striped grass mouse
171.) (Lemniscomys striatus) Typical striped grass mouse
172.) (Dremomys pernyi) Perny's ground squirrel
173.) (Heliosciurus rufobranchiatus) Red-legged sun squirrel
174.) (Ratufa affinis) Cream-coloured giant squirrel
175.) (Xerus rutilus) Unstriped ground squirrel
176.) (Petaurista petaurista) Red giant flying squirrel
177.) (Cricetomys emini) Emin's Pouched Rat
178.) (Gerbillus andersoni) Anderson´s gerbil
179.) (Gerbillus simonii) Simon´s gerbil
180.) (Meriones arimalius) Arabian jird
181.) (Meriones shawi) Lesser Shaw's jird
182.) (Microtus subterraneus) European pine vole
183.) (Cuniculus taczanowskii) Mountain paca
184.) (Dasyprocta fuliginosa) Black agouti
185.) (Hystrix pumila) Phillipine short-tailed porcupine
186.) (Heliophobius argenteocinereus) silvery mole rat
187.) (Allactaga elater) Small five-toed jerboa
188.) (Cannomys badius) Lesser bamboo rat
189.) (Coendou bicolor) Bicolored-spined Porcupine
190.) (Dinomys branickii) Pacarana
191.) (Funambulus palmarum) Indian Palm Squirrel
192.) (Neotamias dorsalis) cliff chipmunk
193.) (Neotamias quadrivittatus) Colorado chipmunk
