Mikan Enikki- an anime about talking, orange cat and his animal buddies.
Wolfs rain- the main characters are wolves, who can turn into humans and they search for their paradise.
Jungle Book Shōnen Mowgli- the adventures of Mowgli, who is raised by wild animals living in jungle
Kimba- a story about white lion, something similar to Lion King.
Porco Rosso- anime movie from Studio Ghibli about a pig who was a pilot
Pom Poko- also Studio Ghibli work, about raccoons who want to save their forest from humans.
Mononoke hime- again Ghibli, a human girl lives with wolves and also protects her forest from evil, greedy humans.
Ponyo- again Ghibli, a story about a fish, which becames a little girl.
My neighbour Totoro- again Ghibli, a family moves to new village and the two girls make friends with gigant bear-alike creature, which they call Totoro.
Last unicorn- anime-alike story about unicorn princess.
Tonde Buurin Super Pig- anime about a girl who turns into magical warrior like Sailor Moon, but unlike to Usagi and other Sailor Senshi, she is a pig after her transformation.
Besides there are many anime with characters who have some animal features, like ears or tails. Those are Wolf and Spice, Di gi charat, Hyper Police, Inuyasha or Utawarerumono. And of course, there is Pokemon in which people catch and train weird animals with supernatural powers.