I can't believe I missed this thread when it first went around, Generally I don't agree with killing for the sake of killing, in my opinion if you like to hunt ( I do ), hunt game that you can use or give away to someone that will, I understand the practical argument that no meat in the wild goes unused, I just don't believe it's ethical or moral, carrion eaters have managed quite well on their own for most of time, they don't and shouldn't depend on our help.
Pests and predators that are directly affecting ones health, property, or live stock are another story and need to be dealt with where ever and how ever possible as long as it's done safely and as humanely as possible.
As for what's edible in the animal world, most anything that swims, creeps, crawls, wears hair, or flys is eaten somewhere in the world, so most species are edible, and taste good if prepared right, that said, the old saying "you are what you eat" should be taken as a caution, some things because of their diet can make you sick, either for a day or two, or permanently (if you get my drift) .
Having spent many weeks in hunting and fishing camps over most of my life time (we always harvested something for camp food when the opportunity presented itself) I eaten a lot of stuff that some folks would pass on, Beaver (meat & tail), Snake, Porcupine, wild Rabbit, Squirrel (greys), Raccoon, Woodchuck, Wildcat, and many species of wild game birds, I and my hunting buddies have always had the benefit of good cooks, plus, almost anything can be made to taste good with the right amount of salt, pepper, and a lot of garlic, so all of the above was fine eating.
On the other hand some critters I've tried once and will never eat again if I can help it, one of which is Possum, I know folks in the south swear how good they are, maybe they know some secret way of fixing and cooking them that we Northerners don't.
In my area of the North East Black Bear is a game animal, it's hunted for it's hide and for it's meat, it's one of those meats that benefit from low and slow cooking, think slow cooker or better yet a pressure cooker, also makes good wild sausage.
Carp, while I'm sure some folks around hear eat it, most consider it a trash fish, though some species are held high on the list of game fish for the sport of catching them, Bluegills and other panfish are considered by many here to be great eating.
Berbot is a puzzle to me, I have lived most of my life in the same area of southern NE, it's predominately French Canadian in ethnicity with a good helping of Italian and Irish thrown into the mix, we do have a fish that we call a "Budbut" (sic), the more commonly know name is Bullheads or Black Catfish, they are ugly, damned near impossible to kill, but they are excellent eating panfried in butter, if you get them out of clean water.