Muskrat was still consumed by old timers back in Michigan when I was a boy, it was somewhat looked down upon though, even by the mid 80s, as not being very good culinary fare. Rabbit of course was tasty, and served at some rural diners when I was growing up.
One of the Marine armorers that is a friend of mine - the guy who ended up with my Gew 88 - kills and eats all sorts of small animals. His theory is that if it has fur and runs around, just cook it enough.
The usual problem with some of the creatures that eat... well less savory things... is a gamey taste. Slow cooking can help. Or tabasco sauce I suppose.
Cats don't have a lot of meat on them. They don't taste exactly like rabbit, but the meat tends to be fairly good quality. You do have to worry about rabies. Ground up with some spices, eh, you wouldn't really think it was cat. That is of course if you were the sort of person bothered by eating cats. I only remember having it once, made into sloppy Joes - long story. I didn't notice anything odd about the taste at the time. If you want to try some, Pounces brand kitty treats work well as bait. That stuff seems like crack to strays.
Season it up and you might think dog meat is some sort of other meat. It does go into the mystery meat category since you find yourself wondering - depending on how it was prepared - whether that is beef, or lamb, or what is that... Bit tough, but no worse than some steaks at the buffet. Might have been an old dog too. I don't imagine that the cute and useful/spry ones end up on the table, but I could be wrong.
Rat on a stick, if they were domestically raised rats, is a lot like a mystery chicken kabob on a stick. All meats are better for being on a stick though. It's sort of like the dark meat on factory raised chickens that isn't really that dark but isn't white meat either. Teriyaki flavoring works well, or something to give it a smokey taste. If you don't know what it was - ie you're just eating a nice chunk of it (filet of rat?) and not a carbonized furry critter with a shaft threw it, eh, you wouldn't know you were eating it. I suppose you could get rabies or worms or something, which might be why I've only seen it served as well done gray mystery chunks.
I remember bear being greasy, squirrel unremarkable. Alligator and snake and frog legs... not exactly like chicken, but yeah, sort of.
At least that's what the other guys in camp said. I couldn't bring myself to eat a beastie that is known to carry tuberculosis! Those in the know say possum's pretty greasy. Not near as good as dog, though!
)
........
Maybe it was out of season.
