My favorite recently extinct mammals by type

Marsupial: Thylacine (1936)

Manatee: Steller's sea cow (Late 1760's)

Rodent: Bulldog rat (1903)

Lagomorph: Sardinian pika (1774)

Nesophont: West Cuban nesophont (1506)

Bat: Guam flying fox (1968)

Primate: Jamaican monkey (1600's)

Ungulate: Auroch (1627)

Carnivore: Giant fossa (Early 1500's)