Another three way tie! I promise you the entire list is not ties! I am glad to see so much animal variety throughout this list, it's a lot of fun.
32 (tie)
Votes: 2 Points: 46 Highest vote: 9 (@WildcatJF )
Archimedes (The Sword in the Stone)
Sword in the Stone tells the story of the young boy Wart's journey to become King Arthur. Along the way Wart has quite the variety of tasks and adventures and is turned into animals because... uh... it was fun to animate? It really is a fun movie. Archimedes is a grump and is always pointing out Merlin and Wart's flaws. But when things go wrong Archimedes swoops in to help in ways that range from literally swooping in to helping Wart learn to read and write.
A scene I remember very well from when I was a kid is below, where Wart is turned into a bird and Archimedes helps him learn to fly and evade a hawk (with questionable success on the second one).
32 (tie)
Votes: 2 Points: 46 Highest vote: 4 (@WildcatJF )
Yakul (Princess Mononoke)
Yakul is the mount of Ashitaka, the banished protagonist of Princess Mononoke who is trying to cure a curse. Yakul doesn't speak and generally behaves like your standard horse (although quite well-trained) but has a lot of personality and the bond between these two is beautiful and sincere.
I also want to point out that there is an almost identical Yakul in the graphic novel
Shuna's Journey, one of Miyazaki's earlier graphic novels. The story has some similarities and I've heard some people call it a prototype Princess Mononoke, but it is quite different. I recommend reading it if you haven't!
32 (tie)
Votes: 2 Points: 46 Highest vote: 10 (@jpfriction )
Zero (Nightmare before Christmas)
Zero is the spooky and cute ghost dog of Jack in Nightmare Before Christmas. Similar to your classic "person wearing a sheet", Zero is made of ghostly fabric with a bright pumpkin nose. Despite being a Halloween-based creature Zero takes on the role of Rudolph for Jack's team when he tries to be Santa.
From a technical side, Zero looks quite different from all the purely stop-motion characters, an effect which I really love. This was done by essentially having Zero staged in a different area than the other characters, but then reflecting him into the camera using a combination of a beam splitter and some special filters.
On another note good grief is it impossible to search for things related to this movie at this time of year, there is so much merch, it overwhelmed any results about the actual movie.