Many animals have been referred to in Hindu scriptures, such as   Cow,  Crocodile,  Dog,  Donkey,  Elephant,  Horse,  Lion,  Matsya,  Naag
Here are some more animals --

Deer
One animal is deer, which has also been mentioned in our scripture.

(1) Jadbharat Born as Deer
The first reference we get of a deer in Bhaagvat Puraan, 5/2. It is of Jadbharat. He was a great Yogee. He left his kingdom and went to forest. One day he found a deer cub drowning in a river. He saved him and brought it up. He got so much attached to it that once when he did not find him, he died and was reborn as a deer.

(2) Seetaa Sees a Golden Deer
The second reference we get from Raamaayan, when Raavan wanted to abduct Seetaa, he asked Maarech to appear before Her as an enchanted golden deer. He did so and as Seetaa saw that deer She asked Raam to bring it for Her. Raam killed it, but Maareech called upon Lakshman and Seetaa, so Seetaa got scared and She sent Lakshman to help Raam. After Lakshman left, Raavan abducted Seetaa.

(3) Yayaati Sees an Extraordinary Deer
Another reference is of Raajaa Yayaati. This name is unknown to most people in relation to seeing an extraordinary deer in a forest. When Naarad Jee praised Yayaati to Indra, Indra got worried and he thought to invite him to Swarg, so he sent a messenger with his Saarathee Maatali. Yayaati talked to Maatali and decided not to go to Swarg, and preferred rather to convert this Prithvi into Swarg. He sent his messengers all over to follow his instructions that they should meditate only upon Vishnu and be happy. Whoever will not follow his teachings he will be considered as thief and will be punished. People started doing it and they lived happily. Even after living for 100,000 years he looked as young as of a 25 years young man.

This worried Indra. After Maatali failed to bring Yayaati to Swarg, he took help of Kaam Dev to bring the King to Swarg. Kaam Dev succeeded in forgetting his Dharm and sprouting the feelings of desires in his heart. One day when he went to a forest for hunting, he saw an extraordinary deer in the forest. He had four horns and was extraordinarily beautiful. King followed him, and that deer took him far away (as Raam's deer took Him away) in the forest. This was a trick to get Yayaati into trouble so that he forgets everything and comes to Swarg Lok.
[Padm Puraan, 2/13]

(4) Rishyashring - the Son of a Deer
Rishi Rishyashring, son of Vibhaandak Muni, who helped in performing the Putreshti Yagya for Dasharath, was also born from a she-deer.
[MBH, 0-4-Van/19]

(5) Mrig: the Ride of Vaayu Dev
Mrig is the ride of Vaayu Dev.
[Skand Puraan, 1/1]

Tortoise
Tortoise is another animals which is very much mentioned in Hindi scriptures.

(1) Vishnu's Incarnation
Tortoise, the Kashchap Avataar is Vishnu's second (the first incarnation was of Matsya - Fish) incarnation. Vishnu took this Avataar at the time of Saagar Manthan to stabilize the Mandaraaachal Parvat used as the churning rod to churn the Ksheer Saagar.
[MBH, Saagar Manthan]

(2) Food for Garud Jee
His another reference is in context of Garud Jee. As soon as Garud Jee was born, he decided to free his mother Vinataa from the slavery of her sister. He had to bring Amrit for that. As he felt hungry, he asked his mother something to eat. Seeing his body, Vinataa directed him to go to his father Kashyap Jee and ask for the food from him. So he went to Kashyap Jee and asked him some food to eat. Kashyap Jee directed him to an island where an elephant and a tortoise lived under the curse of each other. Garud Jee ate both of them.
[MBH, G-0-Prolog/7]

(3) Longevity
He is mentioned for his long life. It is believed that a tortoise age is over 250 years.

(4) In Indian Philosophy
There are two contexts in which he is mentioned in philosophical sense --His another reference is regarding its philosophy. His mention is made especially in the reference of a Gyaanee (learned and wise) man. His simile is given - as the tortoise pulls his hands and feet inside and sits quietly without being affected of all outside things or his environment, in the same way a human being should also pull his all Indriyaan from outwardly pleasures of the world and meditate on Bhagavaan.