I've always cared about adding new mammal species, and it wasn't until 2020 that I started keeping track of which families I'd seen. It was natural next step for me to see how many genera I've seen.
I made this list over a year ago. I added any additions from the past year to the bottom so those few aren't in taxonomic order.
Google says there are around 1,258 extant mammal genera, With 683, I've seen a little over 54%
1. Zaglossus
2. Tachyglossus
3. Ornithorhynchus
4. Caluromys
5. Marmosa
6. Monodelphis
7. Chironectes
8. Didelphis
9. Philander
10. Marmosops
11. Dromiciops
12. Myrmecobius
13. Dasyuroides
14. Parantechinus
15. Dasyurus
16. Sarcophilus
17. Antechinus
18. Phascogale
19. Sminthopsis
20. Macrotis
21. Isoodon
22. Perameles
23. Peroryctes
24. Phascolarctos
25. Vombatus
26. Lasiorhinus
27. Burramys
28. Cercartetus
29. Trichosurus
30. Ailurops
31. Strigocuscus?
32. Phalanger
33. Spilocuscus
34. Pseudocheirus
35. Dactylopsila
36. Petaurus
37. Acrobates
38. Distoechurus
39. Hypsiprymnodon
40. Aepyprymnus
41. Bettongia
42. Potorous
43. Dorcopsis
44. Onychogalea
45. Thylogale
46. Dendrolagus
47. Petrogale
48. Setonix
49. Lagorchestes
50. Wallabia
51. Macropus
52. Osphranter
53. Notamacropus
54. Dasypus
55. Euphractus
56. Chaetophractus
57. Priodontes
58. Cabassous
59. Tolypeutes
60. Myrmecophaga
61. Tamandua
62. Cyclopes
63. Choloepus
64. Bradypus
65. Dugong
66. Trichechus
67. Procavia
68. Heterohyrax
69. Dendrohyrax
70. Loxodonta
71. Elephas
72. Orycteropus
73. Rhynchocyon
74. Macroscelides
75. Petrodromus
76. Elephantulus
77. Galegeeska
78. Chrysochloris
79. Echinops
80. Setifer
81. Tenrec
82. Hemicentetes
83. Nesogale
84. Microgale
85. Ochotona
86. Pronolagus
87. Romerolagus
88. Bunolagus
89. Sylvilagus
90. Poelagus
91. Oryctolagus
92. Lepus
93. Castor
94. Perognathus
95. Chaetodipus
96. Dipodomys
97. Thomomys
98. Geomys
99. Anomalurus
100. Pedetes
101. Ctenodactylus
102. Atherurus
103. Hystrix
104. Petromus
105. Heterocephalus
106. Heliophobius
107. Georychus
108. Fukomys
109. Erethizon
110. Coendou
111. Cuniculus
112. Cavia
113. Galea
114. Hydrochoerus
115. Kerodon
116. Dolichotis
117. Pediolagus
118. Dasyprocta
119. Myoprocta
120. Lagostomus
121. Chinchilla
122. Lagidium
123. Dinomys
124. Ctenomys
125. Octodon
126. Spalacopus
127. Plagiodontia
128. Capromys
129. Myocastor
130. Hoplomys
131. Proechimys
132. Ratufa
133. Funambulus
134. Tamiops
135. Dremomys?
136. Sundasciurus
137. Lariscus
138. Callosciurus
139. Tamiasciurus
140. Sciurus
141. Microsciurus
142. Glaucomys
143. Iomys
144. Hylopetes
145. Petaurista
146. Pteromys
147. Xerus
148. Geosciurus
149. Euxerus
150. Sciurotamias
151. Neotamias
152. Tamias
153. Eutamias
154. Ammospermophilus
155. Urocitellus
156. Callospermophilus
157. Ictidomys
158. Poliocitellus
159. Otospermophilus
160. Xerospermophilus
161. Spermophilus
162. Marmota
163. Cynomys
164. Heliosciurus
165. Funisciurus
166. Paraxerus
167. Graphiurus
168. Glirulus
169. Glis
170. Muscardinus
171. Dryomys
172. Eliomys
173. Sicista
174. Zapus
175. Salpingotus
176. Euchoreutes
177. Allactaga
178. Jaculus
179. Typhlomys
180. Rhizomys
181. Cannomys
182. Tachyoryctes
183. Nannospalax
184. Calomyscus
185. Brachytarsomys
186. Eliurus
187. Macrotarsomys
188. Hypogeomys
189. Nesomys
190. Beamys
191. Cricetomys
192. Dendromus
193. Poemys
194. Phodopus
195. Mesocricetus
196. Cricetulus
197. Cricetus
198. Ondatra
199. Craseomys
200. Clethrionomys
201. Lagurus
202. Arvicola
203. Microtus
204. Neotoma
205. Reithrodontomys
206. Peromyscus
207. Habromys
208. Sigmodon
209. Reithrodon
210. Zygodontomys
211. Nephelomys
212. Oecomys
213. Oligoryzomys
214. Akodon
215. Rhipidomys
216. Thomasomys
217. Irenomys
218. Abrothrix
219. Auliscomys
220. Nyctomys
221. Ototylomys
222. Acomys
223. Deomys
224. Lophuromys
225. Gerbilliscus
226. Taterillus
227. Desmodillus
228. Gerbillus
229. Pachyuromys
230. Sekeetamys
231. Meriones
232. Psammomys
233. Phloeomys
234. Crateromys
235. Chiropodomys
236. Hydromys
237. Melomys
238. Uromys
239. Leporillus
240. Mesembriomys
241. Notomys
242. Pseudomys
243. Otomys
244. Parotomys
245. Arvicanthis
246. Grammomys
247. Lemniscomys
248. Micaelamys
249. Rhabdomys
250. Thallomys
251. Apodemus
252. Mus
253. Mastomys
254. Micromys
255. Niviventer
256. Rattus
257. Leopoldamys
258. Lenothrix
259. Maxomys
260. Sundamys
261. Tupaia
262. Galeopterus
263. Microcebus
264. Mirza
265. Cheirogaleus
266. Phaner
267. Lepilemur
268. Hapalemur
269. Prolemur
270. Lemur
271. Eulemur
272. Varecia
273. Avahi
274. Propithecus
275. Indri
276. Daubentonia
277. Galagoides
278. Galago
279. Paragalago
280. Otolemur
281. Perodicticus
282. Loris
283. Nycticebus
284. Cephalopachus
285. Tarsius
286. Cebuella
287. Mico
288. Callimico
289. Callithrix
290. Saguinus
291. Leontopithecus
292. Saimiri
293. Sapajus
294. Cebus
295. Aotus
296. Callicebus
297. Cheracebus
298. Plecturocebus
299. Pithecia
300. Chiropotes
301. Cacajao
302. Alouatta
303. Ateles
304. Lagothrix
305. Brachyteles
306. Macaca
307. Cercocebus
308. Mandrillus
309. Lophocebus
310. Papio
311. Theropithecus
312. Allenopithecus
313. Miopithecus
314. Erythrocebus
315. Chlorocebus
316. Allochrocebus
317. Cercopithecus
318. Colobus
319. Piliocolobus
320. Presbytis
321. Rhinopithecus
322. Nasalis
323. Semnopithecus
324. Trachypithecus
325. Hoolock
326. Hylobates
327. Nomascus
328. Symphalangus
329. Pongo
330. Gorilla
331. Pan
332. Homo
333. Erinaceus
334. Atelerix
335. Paraechinus
336. Hemiechinus
337. Hylomys
338. Sorex
339. Cryptotis
340. Blarina
341. Neomys
342. Suncus
343. Diplomesodon
344. Mogera
345. Solenodon
346. Cynopterus
347. Thoopterus
348. Eonycteris
349. Rousettus
350. Lissonycteris
351. Hypsignathus
352. Epomops
353. Epomophorus
354. Macroglossus
355. Eidolon
356. Pteropus
357. Rhinopoma
358. Lavia
359. Cardioderma
360. Megaderma
361. Macroderma
362. Triaenops
363. Paratriaenops
364. Macronycteris
365. Hipposideros
366. Rhinolophus
367. Taphozous
368. Emballonura
369. Paremballonura
370. Coleura
371. Cormura
372. Balantiopteryx
373. Cyttarops
374. Diclidurus
375. Peropteryx
376. Centronycteris
377. Rhynchonycteris
378. Saccopteryx
379. Nycteris
380. Myzopoda
381. Noctilio
382. Furipterus
383. Thyroptera
384. Mormoops
385. Pteronotus
386. Macrotus
387. Micronycteris
388. Desmodus
389. Diaemus
390. Trachops
391. Lophostoma
392. Phyllostomus
393. Chrotopterus
394. Mimon
395. Vampyrum
396. Glossophaga
397. Leptonycteris
398. Erophylla
399. Anoura
400. Hylonycteris
401. Choeronycteris
402. Lonchophylla
403. Carollia
404. Sturnira
405. Vampyriscus
406. Uroderma
407. Vampyrodes
408. Platyrrhinus
409. Ectophylla
410. Artibeus
411. Dermanura
412. Natalus
413. Mormopterus
414. Molossus
415. Eumops
416. Otomops
417. Mops
418. Tadarida
419. Miniopterus
420. Cistugo
421. Pipistrellus
422. Vespertilio
423. Tylonycteris
424. Neoromicia
425. Laephotis
426. Lasionycteris
427. Histiotus?
428. Eptesicus
429. Parastrellus
430. Perimyotis
431. Antrozous
432. Rhogeessa
433. Plecotus
434. Corynorhinus
435. Aeorestes
436. Dasypterus
437. Lasiurus
438. Scotophilus
439. Nycticeius
440. Murina?
441. Myotis
442. Phataginus
443. Manis
444. Nandinia
445. Neofelis
446. Panthera
447. Pardofelis
448. Catopuma
449. Leptailurus
450. Caracal
451. Leopardus
452. Lynx
453. Acinonyx
454. Puma
455. Herpailurus
456. Otocolobus
457. Prionailurus
458. Felis
459. Prionodon
460. Viverricula
461. Civettictis
462. Viverra
463. Genetta
464. Arctogalidia
465. Arctictis
466. Paguma
467. Paradoxurus
468. Cynogale
469. Chrotogale
470. Hemigalus
471. Crocuta
472. Hyaena
473. Parahyaena
474. Proteles
475. Cynictis
476. Rhynchogale
477. Bdeogale
478. Ichneumia
479. Herpestes
480. Atilax
481. Urva
482. Suricata
483. Crossarchus
484. Helogale
485. Mungos
486. Cryptoprocta
487. Fossa
488. Galidia
489. Galidictis
490. Mungotictis
491. Urocyon
492. Otocyon
493. Nyctereutes
494. Vulpes
495. Chrysocyon
496. Speothos
497. Cerdocyon
498. Lycalopex
499. Lupulella
500. Lycaon
501. Cuon
502. Canis
503. Ailuropoda
504. Tremarctos
505. Helarctos
506. Melursus
507. Ursus
508. Callorhinus
509. Arctocephalus
510. Neophoca
511. Otaria
512. Eumetopias
513. Zalophus
514. Odobenus
515. Neomonachus
516. Mirounga
517. Hydrurga
518. Halichoerus
519. Pagophilus
520. Phoca
521. Pusa
522. Ailurus
523. Bassaricyon
524. Bassariscus
525. Nasua
526. Nasuella
527. Potos
528. Procyon
529. Mydaus
530. Conepatus
531. Mephitis
532. Spilogale
533. Taxidea
534. Mellivora
535. Arctonyx
536. Meles
537. Pekania
538. Eira
539. Gulo
540. Martes
541. Melogale
542. Galictis
543. Vormela
544. Ictonyx
545. Poecilogale
546. Pteronura
547. Lontra
548. Enhydra
549. Hydrictis
550. Lutra
551. Aonyx
552. Lutrogale
553. Mustela
554. Neogale
555. Equus
556. Ceratotherium
557. Diceros
558. Rhinoceros
559. Dicerorhinus
560. Tapirus
561. Lama
562. Camelus
563. Babyrousa
564. Phacochoerus
565. Hylochoerus
566. Potamochoerus
567. Sus
568. Catagonus
569. Dicotyles
570. Tayassu
571. Hippopotamus
572. Choeropsis
573. Moschiola
574. Tragulus
575. Moschus
576. Elaphodus
577. Muntiacus
578. Axis
579. Dama
580. Rusa
581. Cervus
582. Elaphurus
583. Rucervus
584. Hydropotes
585. Capreolus
586. Alces
587. Rangifer
588. Odocoileus
589. Blastocerus
590. Ozotoceros
591. Hippocamelus
592. Pudu
593. Mazama
594. Bos
595. Bubalus
596. Syncerus
597. Boselaphus
598. Tetracerus
599. Tragelaphus
600. Nesotragus
601. Aepyceros
602. Raphicerus
603. Antidorcas
604. Litocranius
605. Saiga
606. Antilope
607. Nanger
608. Gazella
609. Eudorcas
610. Madoqua
611. Ourebia
612. Redunca
613. Kobus
614. Pelea
615. Hippotragus
616. Addax
617. Oryx
618. Alcelaphus
619. Beatragus
620. Damaliscus
621. Connochaetes
622. Oreamnos
623. Budorcas
624. Ammotragus
625. Arabitragus
626. Hemitragus
627. Pseudois
628. Capra
629. Ovis
630. Rupicapra
631. Naemorhedus
632. Capricornis
633. Ovibos
634. Sylvicapra
635. Philantomba
636. Cephalophus
637. Oreotragus
638. Antilocapra
639. Giraffa
640. Okapia
641. Eubalaena
642. Eschrichtius
643. Balaenoptera
644. Megaptera
645. Physeter
646. Inia
647. Delphinapterus
648. Leucopleurus
649. Lagenorhynchus
650. Sagmatias
651. Orcaella
652. Orcinus
653. Delphinus
654. Sotalia
655. Sousa
656. Stenella
657. Steno
658. Tursiops
659. Globicephala
660. Feresa
661. Grampus
662. Pseudorca
663. Cephalorhynchus
664. Neophocaena
665. Phocoena
New over the past year:
666. Pectinator
667. Metachirus
668. Pontoporia
669. Abrocoma
670. Sciurocheirus
671. Thylamys
672. Zaedyus
673. Calomys
674. Oxymycterus
675. Holochilus
676. Lophiomys
677. Dorcatragus
678. Ammodorcas
679. Eligmodontia
680. Microcavia
681. Nyctalus
682. Ammodillus
683. Euderma