As far as the 70 listed Mammal species are concerned:
In Captivity / Successful Ex-Situ Breeding Programmes (21):
(* indicates re-introduced to wild)
Dibbler*
Gilbert's Potoroo*
Numbat*
Carpentarian Rock Rat
Vancouver Island Marmot*
Pygmy Hog*
Visayan Spotted Deer
Bawean Deer
Dama Gazelle*
Slender-horned Gazelle
Addax*
Arabian Oryx*
Wild Bactrian Camel* (breeding programme at Zakhyn Us, Mongolia)
African Wild Ass
Przewalski's Wild Horse*
Black-Footed Ferret*
Giant Panda*
Iberian Lynx*
Red Wolf*
Black Lion Tamarin
Golden Lion Tamarin*
Well Managed In-Situ Programmes / Semi-Captive Sanctuaries Exist (6):
(the establishment of captive groups for most species also in varying stages of development)
Northern Hairy-Nosed Wombat (? possibly now a small captive group too)
Scott's Tree Kangaroo? (no plans for captivity; wild managed pop. rising)
Mount Claro Rock Wallaby
Ethiopian Wolf
Hirola (48+ in fenced conservancy)
White-Headed Langur (3 also in captivity; no breeding)
Only Further Ex-Situ Programme Development Required (1):
Madeira Pipistrelle
Good Targets for Captive Breeding Programmes (No Current Captive Individuals) (9):
Central Rock Rat (previous captive colony established, but died out 2011)
Santa Catarina's guinea pig (captive individuals kept previously; current?)
Walia Ibex
Saola (at least, a managed semi-captive population)
Tamaraw (Mindoro Dwarf Buffalo) (a failed captive programme attempted late '90s)
Northern Muriqui (given success with Southern Muriqui in captivity)
Cozumel Raccoon
Blond Titi Monkey? (success with other Callicebinae sp.)
Bonin Flying Fox (previously attempted at Tama Zoo, Tokyo)
Possibly Suitable for Ex-Situ Breeding Programmes? (Never in Captivity) (13)
(alas, my understanding of bat biology and captive husbandry is lacking, many of the bats here may actually be difficult / unsuitable)
Cozumel Harvest Mouse
Jico Deer Mouse
San Quintin Kangaroo Rat
Riverine Rabbit
Perrier's Sifaka?
Bulmer's Fruit Bat
Fernandez's Sword-Nosed Bat
Flat-Headed Myotis
Jamaican Flower Bat
Kolar leaf-nosed bat
Seychelles Sheath-Tailed Bat
Yemeni Mouse-Tailed Bat
Population Too Low to Consider Ex-Situ (3):
(Number of captures required for captive pop. too considerable a proportion of existing 'steady' ex-situ population)
Hainan Gibbon
Cao-vit Crested Gibbon
Javan Rhino (borderline, given Ujung Kulon pop. nearing carrying capacity; some transfer to semi-captive conditions may soon be required)
Diet-Restrictive / Too Difficult for Ex-Situ (1):
Northern Sportive Lemur
Data-Deficient / Biology and/or Pop. Poorly Known (6):
(considerably more in-situ work required first)
Golden-Mantled Tree Kangaroo
Fijian Monkey-Faced Bat
Dryas Monkey (? or 'possible ex-situ')
Andean Caenolestid
Cohen's Horseshoe Bat
Myanmar Snub-Nosed Monkey
Likely Already Extinct (and last confirmed sighting) (11):
Wondiwoi Tree-Kangaroo (1928)
Dwarf Hutia (1937)
Little Earth Hutia (1978)
Christmas Island Shrew (1985)
Kouprey (1969-1970)
Puebla Deer Mouse (1957)
Telefomin Cuscus (~1997)
Montane Monkey-Faced Bat (1990)
Emperor Rat (1888)
Guadalcanal Rat (1888)
Malabar Large-Spotted Civet (1990)
____
With that quick assessment, that's about 10-15ish species currently not held in captivity that we know would likely benefit from, and result in, a reasonably successful ex-situ breeding programme (e.g. ethiopian wolf, hirola, walia ibex etc.).
Then there's those species (e.g. a number of rodents, bats and a sifaka) that may just about cut it too, all things considered (current population, known biology and diet, comparison with similar captive species etc. unless I'm mistaken). The rest are species whose husbandry we understand and already fare well in captivity or, in contrast, generally species we know far too little about to adequately assess suitability.
Let me know if anything needs correcting, folks. Will be constantly updating as I find more information.