According to ACVO's publication Ocular disorders presumed to be inherited in dogs (1999), cherry eye (prolapsed gland of the third eyelid) has been identified as a known or suspected inherited disorder in the following breeds: Beagle, Bloodhound, Bulldog (English), Chinese shar pei, Cocker spaniel, Lhasa apso, Newfoundland. ACVO's breeding advice regarding cherry eye is that it's "breeder option", meaning that the entity is suspected of being inherited but does not represent potential compromise of vision or other ocular function.
Edited to add the prevalence of cherry eye reported in BHCA's 1998 Health Survey was approximately 5%.
[ March 10, 2004, 11:44 PM: Message edited by: Betsy Iole ]