Won't Ever Kill : Foxes, Horses, Pappies (One time I accidentally killed a fox, and was so upset I made it my undead thrall so I could pretend it wasn't dead)
Rarely Kill : Chickens, Goats
Kill if they bug me : Mudcrabs, Skeevers, Wolves, Bears, Sabre-Tooth Tiggies
Blast on Sight : Bunnies, Mammoths, Horkers
Chase Incessantly Across Landscape with Knife in Murderous Frenzy : Venisons (i.e. Deer of all kinds), Argonians
The last one is a throw-over habit from Oblivion, where it was easier due to Speed and Athletics, but the lack of such skills in Skyrim hasn't stopped me. The moment I spot any sort of deer, the hunt is officially on... and everything else is secondary. Sometimes I don't even bother with the knife, and chase elks down to punch them to death and harvest their sweet meats...

...... Then I eat the venison, snap out of the hunter's frenzy, and wonder where the hell I got to and what I was doing before VENISON!!
Does take me back to many days spent chasing Venisons across the entire length of Cyrodill, swinging my little knife around like a hokerr, jumping off cliffs onto them, etc. I've been killed many times while hunting Venisons, simply due to complete lack of self-preservation instincts in the hunting frenzy.