If you're looking for anime similar to Match Uri no Shoujo, you might like these titles.
Hector the Rat teams up with his fellow denizens of Pretty Wood, including the titular Coral (a young girl) and the unimaginatively named Crow (a crow), to head off to Holland.
Once upon a time a childless King and Queen were finally blessed with a beautiful daughter. However, the celebrations were cut short when a witch appeared cursing the child to die on her sixteenth birthday by the prick of a spinning wheel – at least, so the tale tells us. In reality the wicked witch was a one-legged man whose very presence struck fear into the Queen, and the magical curse was a fabrication to cover up the truth. On her fifteenth birthday, the young princess discovers her mother’s old diary and learns that the man was the Queen’s first love. Intrigued by the man her mother so adored, she decides to pay him a visit...
A donkey has grown old and weak after having worked for a human being for a long time. Realizing his prime time has passed, the donkey decides to go to Bremen to join the town musicians. On the way there, he meets a dog, a cat, and a rooster, and they find the robbers’ house. Four animals chase the robbers away from the house. They make their new lives with their new home.