Gaj.  Hast.  Elephant.
There are many mentions in our scriptures about elephants.

Bhavishya Puraan, p 596 -
Eight elephants are said to be born in Dev Yoni - (1) Kumud, (2) Airaavat, (3) Padm, (4) Pushpdant, (5) Vaaman, (6) Suprateek, (7) Anjan, and (8) Saarvbhaum.

[Valmiki Ramayan, 1/6]
Vaalmeeki Jee writes in his Raamaayan about the elephants in Ayodhyaa --
It is said that eight elephants from eight corners called Asht Diggaj support this Universe. And these eight elephants have their presiding deities. From those eight elephants, four are prominent - (1) Airaavat, the Elephant of Indra, (2) Anjan , the Elephant of Varun, the Rain-god, (3) Vaaman, the Elephant of Yam Raaj, the Lord of Death, and (4) Pundareek. Thus, the elephants of Ayodhya have been termed as Divine breed.
       x       x      x       x      x
That city is always full with vigorous and mountain like elephants bred mainly from three classes viz., Bhadra, Mandra and Mrig. And inter-bred among these three main classes are Bhadra-Mandra, Mandra-Mrig, Bhadra-Mrig and the like. The Bhadra is the elephant class for King's ride, called Bhadra Gaj. It is a state elephant with high honors and for occasional or ceremonial use. Mandra and Mrig are classes of breed tamed and used in wars or for the ride of other nobility. These are the essential mammals used for other lifting and carrying works.

[Bhaagvat Puraan, 10/p14]
Kans had a very powerful elephant named Kuvalayaaped whom he prepared to kill Krishn when he invited Krishn to Mathuraa by Akroor Jee for his Dhanush Yagya. He made him drink lots of liquor and got mad to be able to kill Krishn.

Mahaabhaarat,
In Mahaabhaarat, Bhagadatt had a very intelligent elephant who was difficult to be killed. But Arjun killed him and then his owner.

Indra's elephant, Airaavat, is world famous.