There are >1,200 kinds of bats

The most comprehensive list that I have is here. It's a list of 1,116 species, taken from Wilson, D. E. and Reeder, D. M. (2005). Mammal species of the world: a taxonomic and geographic reference. Baltimore: Johns Hopkins University Press.

Of those, I've only seen 99 species, from 16 families:

Emballonuridae

Diclidurus albus, Lamanai, Belize


Rhynchonycteris naso, Tortuguero National Park, Costa Rica


Saccopteryx bilineata, Tortuguero National Park, Costa Rica


Saccopteryx leptura, Lamanai, Belize


Taphozous georgianus, near Rockhampton, Australia


Hipposideridae

Asellia tridens, Hal Tsaror, Israel


Hipposideros commersoni, Kianjavato, Madagascar


Megadermatidae

Macroderma gigas, near Rockhampton, Australia


Miniopteridae

Miniopterus manavi, Kianjavato, Madagascar


Miniopterus schreibersii, near Rockhampton, Australia


Molossidae

Molossus ater, Lamanai, Belize


Tadarida brasiliensis, Austin, Texas


Tadarida teniotis, Sede Boqer, Israel


Mormoopidae

Mormoops megalophylla, Lamanai, Belize


Pteronotus davyi, Lamanai, Belize


Pteronotus parnellii, Lamanai, Belize


Mystacinidae

Mystacina tuberculata, Fiordland National Park, New Zealand


Myzopodidae

Myzopoda aurita, Kianjavato, Madagascar


Natalidae

Natalus tumidirostris, Tamana Cave, Trinidad


Noctilionidae

Noctilio leporinus, Tortuguero National Park, Costa Rica


Pteropodidae

Epomophorus wahlbergi, Sabi Sands, South Africa


Pteropus conspicillatus, Cape Tribulation, Australia


Pteropus poliocephalus, Brisbane, Australia


Pteropus scapulatus, Cape Tribulation, Australia


Rousettus madagascariensis, Kianjavato, Madagascar


Phyllostomidae

Ametrida centurio, Point Fortin, Trinidad


Anoura geoffroyi, Tamana Cave, Trinidad


Artibeus cinereus, St. Benedicts, Trinidad


Artibeus intermedius, Lamanai, Belize


Artibeus jamaicensis, Tortuguero National Forest, Costa Rica


Artibeus lituratus, Tortuguero National Forest, Costa Rica


Artibeus obscurus, Tiputini, Ecuador


Artibeus phaeotis, Lamanai, Belize


Artibeus watsoni, Tortuguero National Forest, Costa Rica


Brachyphylla cavernarum, Anguilla, BWI


Carollia brevicauda, Tortuguero National Forest, Costa Rica


Carollia castanea, Tortuguero National Forest, Costa Rica


Carollia perspicillata, Tortuguero National Forest, Costa Rica


Centurio senex, Lamanai, Belize


Desmodus rotundus, Tortuguero National Forest, Costa Rica


Diaemus youngi, Trinidad


Ectophylla alba, Tortuguero National Forest, Costa Rica


Glossophaga commissarisi, Tortuguero National Forest, Costa Rica


Glossophaga soricina, Tortuguero National Forest, Costa Rica


Hylonycteris underwoodi, Tortuguero National Forest, Costa Rica


Lophostoma (Tonatia) saurophila, Tortuguero National Forest, Costa Rica


Micronycteris brachyotis, Tortuguero National Forest, Costa Rica


Micronycteris microtus, Tortuguero National Forest, Costa Rica


Micronycteris schmidtorum, Lamanai, Belize


Mimon crenulatum, Lamanai, Belize


Mimon bennettii, Lamanai, Belize


Monophyllus plethodon, Anguilla, BWI


Phyllostomus hastatus, Tamana Cave, Trinidad


Platyrrhinus helleri, Tortuguero National Forest, Costa Rica


Sturnira lilium, Lamanai, Belize


Sturnira tildae, St. Benedicts, Trinidad


Tonatia brasiliense, Lamanai, Belize


Tonatia evotis, Lamanai, Belize


Trachops cirrhosus, Tortuguero National Forest, Costa Rica


Uroderma bilobatum, Tortuguero National Forest, Costa Rica


Vampyressa nymphaea, Tortuguero National Forest, Costa Rica


Vampyressa pusilla, Lamanai, Belize


Rhinolophidae

Rhinolophus clivosus, Avdat, Israel


Rhinolophus ferrumequinam, near Pierre Perthuis, France


Rhinolophus hipposideros, near Bazoches, France


Rhinolophus megaphyllus, Tocal, Australia


Rhinopomatidae

Rhinopoma hardwickii, hal Tsaror, Israel


Thyropteridae

Thyroptera tricolor, Tortuguero National Forest, Costa Rica


Vespertilionidae

Antrozous pallidus, near Balmorhea Texas, USA


Bauerus dubiaquercus, Lamanai, Belize


Chalinolobus tuberculatus, Fiordland National Park, New Zealand


Eptesicus bottae, Sede Boqer, Israel


Eptesicus furinalis, Lamanai, Belize


Eptesicus fuscus, Toronto, Canada


Lasionycteris noctivagans, Elk Island Provincial Park, Canada


Lasiurus cinereus, Toronto, Canada


Lasiurus ega, Lamanai, Belize


Myotis albescens, Tiputini, Ecuador


Myotis elegans, Lamanai, Belize


Myotis emarginatus, near Pierre Perthuis, France


Myotis goudoti, Kianjavato, Madagascar


Myotis keaysii, Lamanai, Belize


Myotis keenii, Sooke, Canada


Myotis leibii, near Chaffey's Lock, Canada


Myotis lucifugus, Edmonton, Canada


Myotis nigricans, Tortuguero National Forest, Costa Rica


Myotis septentrionalis, Glacier National Park, Canada


Myotis velifer, Eckert James River Bat Cave Preserve, Texas


Myotis yumanensis, Squilax, Canada


Nyctophilus geoffroyi, Tocal, Australia


Nyctophilus gouldi, Tocal, Australia


Otonycteris hemprichii, Sede Boqer, Israel


Pipistrellus bodenheimeri, Hal Tsaror, Israel


Pipistrellus capensis, Sabi Sands, South Africa


Pipistrellus kuhlii, Sede Boqer, Israel


Pipistrellus ruepellii, Hal Tsaror, Israel


Pipistrellus subflavus, Gainesville, TX, USA


Rhogeesa tumida, Lamanai, Belize


Scotophilus dinganii, Sabi Sands, South Africa