Deer family members
Any deer family member can contract CWD. That is, any split-hoofed, branching-antlered mammal. Not goats. Not antelopes. They have horns, not antlers.
So. Deer, certainly. Elk, certainly. Also moose, Sika deer, Fallow deer, red stags, and any others of that family. (family Cervidae, for the biologists)
There is no proof that CWD can be passed to humans. In areas in the West where CWD has been endemic for years, the statistical occurrance of CJD (Creutzfeldt-Jakob Disease, a similar disease in humans) is the same as in areas where CWD has never been found in deer.
OTOH, I sure wouldn't care to be the one person who proved that particular statistic wrong!!
Now Mad Cow disease IS transmissible from cattle to humans, but most TSE's (transmissible spongiform encephalopathies--aren't you glad you asked!) are species-specific. The best example we have is Sheep Scrapie, which is the sheep TSE, and which we have known about for hundreds of years. And shepherds do NOT get sheep scrapie. So the contention that the deer TSE, CWD, is not transmissible to humans is probably correct. However (there is always that darn "however!") it is impossible to prove a negative. We'll just have to wait and see.
As to how long is the incubation period, ZeroJunk's question, that isn't known for sure. It IS known that CJD in humans can have an incubation period of several years. Probably the incubation for CWD is shorter in deer, with their shorter life span.
All of these TSE's are hideous, and yes, I am concerned. But for the present I'm still eating deer meat.