I did consider the possibility of one leg (somewhat unlikely) and no legs (but couldn't find anything in this list that would fit that).
Class Mammalia
Subclass Prototheria: monotremes: echidnas and the platypus
Subclass Theriiformes: live-bearing mammals and their prehistoric relatives.
Infraclass †Allotheria: multituberculates
Infraclass †Triconodonta: triconodonts
Infraclass Holotheria: modern live-bearing mammals and their prehistoric relatives.
Supercohort Theria: live-bearing mammals
Cohort Marsupialia: marsupials
Magnorder Australidelphia: Australian marsupials and the monito del monte
Magnorder Ameridelphia: New World marsupials.
Cohort Placentalia: placentals
Magnorder Xenarthra: xenarthrans
Magnorder Epitheria: epitheres
Grandorder Anagalida: lagomorphs, rodents, and elephant shrews
Grandorder Ferae: carnivorans, pangolins, †creodonts, and relatives
Grandorder Lipotyphla: insectivorans
Grandorder Archonta: bats, primates, colugos, and treeshrews
Grandorder Ungulata: ungulates
Order Tubulidentata incertae sedis: aardvark
Mirorder Eparctocyona: †condylarths, whales, and artiodactyls (even-toed ungulates)
Mirorder †Meridiungulata: South American ungulates
Mirorder Altungulata: perissodactyls (odd-toed ungulates), elephants, manatees, and hyraxes