This article is from the Miscellaneous Cat Information FAQ, posted to rec.pets.cats newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
Most domestic cats purr. But do the big ones? Most people say not, but from The Big Cat:
Assertions have been widely made that the roaring cats above are not able to purr, assertions that have now been disproven. George B. Schaller reports purring in the lion, tiger, and leopard, as well as in the cheetah, but remarks that in the lion the sound is produced only during exhalation and appears to be a much less common vocalization than in the domestic cat . Snow leopards purr, like the house cat, during both exhalation and inhalation . Others have reported that tame, young adult tigers, leopards, jaguars, and cheetahs purr in response to petting. Finally, purring has even been reported in five species of viverrids, as well as suckling black bear cubs and nursing spotted hyenas . These observations are interesting when compared with Gustave Peters' comment that there is still some question about the occurrence of purring, in a strictly defined sense, in the wild cats . He questions whether the noise identified as a purr from the big cats is pthe same in detail and manner of production as the purr of a domestic cat. Of the seven large cats he studied (he did not consider the cheetah), he observed true purring only in the puma, but considered it probable that snow leopards and clouoded leopards also purr. Thus there is still some doubt about the distribution of the ability to purr among the wild cats.
 Ewer, R. F. 1973. THE CARNIVORES. Ithaca, NY: Cornell University Press.
 Hemmer, H. 1972. UNCIA UNCIA. MAMMALIAN SPECIES No. 20, 5 pp.
 Schaller, G. B. 1972. THE SERENGETI LION. Chicago: University of Chicago Press.
 Stuart-Fox, D. T. 1979. MACAN: THE BALINESE TIGER. Bali Post (English edition) July 23, 1979, pp. 12-13.