Crocodile or Makara is of great significance in Hinduism and plays an important role in many famous incidents mentioned in Hindu scriptures. The Vehicle or Vahana of Goddess Ganga is an aquatic animal with the body of a crocodile or Makara and She is believed to travel from the Himalayas to the Bay of Bengal atop a crocodile. The Hindu rain-god Varuna also rides on Makara. Varuna is also the god of the oceans and seas. The God of Love (Kamadeva) has crocodile as his emblem and Rati his wife carries it with her. Kamadeva and Rati are also depicted riding the crocodile.
Please note that Makara as vehicle is not exactly a crocodile it has the body of a crocodile, tail of a fish and sometimes an head with a trunk.
The most popular incident involving a crocodile in Hindu Scriptures is the Gajendra Moksha. Gajendra, a proud elephant, is pulled into the river by a demon in the guise of a crocodile and he tries to escape from it and the struggle continues for several years and finally the elephant prays to Lord Vishnu and the Lord arrives on the scene and rescues the elephant.
Another popular instance of crocodile intervention is in the life of Adi Shankaracharya. Adi Shankara wanted to become a Sanyasi but his mother was dead against it.
One day, while bathing in the Periyar River
His mother was unable to save him and therefore Shankara asked her to give him the permission to renounce the world so that he can be a Sanyasi at the time of his death. Left with no other option, she agreed to it. Shankaracharya recited the mantras of renunciation and immediately, the crocodile left him. After this episode Shankaracharya’s mother gave him the permission to take up Sanyasa.
Another two instances of crocodile in Hindu Scriptures is the incidents involving Lord Hanuman. Once Lord Hanuman was bathing in a lake in the Himalayas and all of a sudden a huge crocodile clasps his legs. With great difficulty he drags the animal out of water. The animal turns itself into a beautiful damsel and proclaims that because of Daksha's curse she became a crocodile and it is Hanuman's contact that revoked the curse.
Similarly, when Hanuman was returning from Lanka his perspiration fell in the mouth of a crocodile and she gave birth to Makaradhwaja.