When I was in New Jersey over Thanksgiving weekend, I birded a park near my parents' home and saw some Egyptian Geese. Their dramatically-marked faces and warm brown bodies made them stand out from the local mob of Canada Geese. Their call is also markedly different: more of a bark than a honk. This was not a new sighting for me, or for the town. Egyptian Geese have persisted at this park for several years since their first appearance in the winter of 2002-2003. I have seen them on and off since then on occasional visits.
Egyptian geese are the only living members of the genus Alopochen, which is part of the shelduck subfamily of Anatidae. The homeland for this species is Africa, where Egyptian geese are widely distributed, from Egypt to South Africa. They were introduced to England and became established there. Individuals may also be found in zoos and private waterfowl collections all over the world. BirdLife considers them a species of Least Concern.
The birds I saw did not migrate by themselves from Africa. The local New Jersey population of Egyptian geese are escapees (or offspring of escapees) from private waterfowl collections. Birders in Central Jersey believe these geese come from free-flying flocks observed at Great Adventure in Jackson. There are probably other local owners of Egyptian Geese as well. While not a common domestic species, they are available for sale on the web (e.g., here and here) and probably from catalogues and local sellers.
Since these birds were free, alive, and unrestrained, and positively identified, the question arises of whether they are countable. Officially, the answer is no, as the species appears on neither the ABA checklist (pdf) nor the New Jersey state list. For an introduced exotic species to be accepted on ABA and local checklists, it must establish a stable self-sustaining breeding population that does not rely on human assistance. While the Egyptian Geese in parks along the Raritan River have been seen with goslings, they hardly qualify as a self-sustaining population because their numbers are so small.
Whatever their status, the geese add an exotic quirk to the local waterfowl population.