I think a 1-year rotating internship might be required by many residency programs. Probably differs a bit among programs. It's also worth noting that zoo, wildlife, and exotics are three separate fields, each with their own residencies and their own policies.
I've heard that the AAZV website has good info for externships and residencies, so you could check there for a list of which universities have zoo residencies and maybe find out what their requirements are. You could also take a look at the match website,
http://www.virmp.org, my memory is that they have descriptions of residency programs and their requirements.
And finally, as far as difficulty of getting in... I've heard of one person who took three years to get into a zoo med residency. She basically did three intern years while re-applying. My understanding was that it's not an uncommon problem, she was a very good candidate. I don't know how wildlife-only or companion exotics residencies stack up that way.
Your question makes it sound like you're interested in non-domestic species in a pretty general way, and that's actually pretty much right where I am, too. In applying to vet schools I asked a lot of zoo/wildlife/exotics faculty members about the breadth of experiences I could get at their schools, and how early I could get hands-on with actual non-domestic cases. I'll pass on a piece of advice that I've gotten over and over again, but I warn you that you're not going to like it: Don't worry so much about trying to get broad experience in your preclinical years; the people the faculty are consistently most impressed with on clinical rotations are the ones with a really strong foundation in small animal internal medicine. There's enough similarity between species that a really sharp diagnostician is a better asset than somebody with a broad cross-species base but little in-depth practical knowledge. And in these fields, letters from well-known people who are impressed with your clinical abilities are apparently very key to getting a residency spot.
