The incarnations of Vishnu is countless. His complete incarnations are ten in number. They are called Dasavataras (the ten incarnations)

1) In the Matsyavatara, (fish incarnation)  the Lord is said to have saved Manu (the progenitor of mankind) and the Saptarsis ( the seven sages, mind-born sons of Brahma) along with their wives during the deluge. Once, while Brahma was reciting the Vedas (the scriptures), an asura named Hayagriva stole the Vedas from the side of Brahma and with them he went under water to the bottom of the ocean and hid himself there. So Mahavishnu decided to take the form of a fish to recover the stolen Vedas. 

2) Lord Vishnu incarnated himself as the Kurma (the tortoise) is order to support the mount Mandara which started sinking during the churning of the ocean (samudramathana).

3) In Varahavatara (boar incarnation) the Lord killed the demon Hiranyaksa and lifted the earth out of the flood waters in which it had been Submerged. This may be a symbolic representation of the extrication of the world from the deluge of sin by the power of the supreme being. 

4) A combination of man and lion, Narasimha represents another form of Vishnu. Narasimha is especially the embodiment of valour which is a divine attribute and hence worshipped by rulers and warriors. When Prahlada, the great devotee of Vishnu was being severely tortured by his father, the demon Hiranyakasipu, Vishnu appeared as Narasimha (man-lion) emerging out of the pillar shown by Hiranyakasipu and killed him. 

5) The next incarnation of Vishnu is Vamana (the dwarf). Bali, a demon, achieved supernatural power by asceticism. To protect the world, Vishnu appeared before him in the form of a dwarf and asked him a favour. Bali granted Vishnu as much land as he could cover in three steps. Vishnu then became a giant. With the first and the second steps he covered the earth and heaven and with the third, he pushed down Bali to the pathala (underworld). Hence he is also known as Trivikrama, one who encompassed the world with three big steps.

6) Parasurama is the sixth Avatara born as the son of the sage-couple, Jamadagni and Renuka. He exterminated the tyrannical among the Kshatriyas led by Kartavirya, who were oppressing the people.

7) Sri Rama, one of the two most popular incarnations of the Lord Vishnu, comes next in the series. As told in the Ramayana, Vishnu came in the form of Rama to rescue the world from the demon, Ravana.

8) Balarama, the elder brother of Sri Krishna, is the eighth incarnation. His adventures include the slaying of the ape Dvivida and the demon Dhenuka, shaking the ramparts of Hastinapura (the capital city of the Pandavas) and dragging the river Yamuna out of its course. 

9) Sri Krishna, the ninth incarnation of Lord Vishnu, is the most popular. He was the charioteer of Arjuna in the battle of Kurukshetra in Mahabharata. To the Hindus, Sri Krishna is the supreme statesman, warrior, hero, philosopher and teacher. He is the great expounder of the 'song celestial', the Bhagavad Gita. 

10) The tenth Avatara is Kalki. It is believed that he will descend upon the earth at the end of the present age (Kali Yuga). Riding on the back of  a white horse, with a drawn sword, he will destroy the enemies of Dharma and re-establish it in all its glory.

The list of incarnations of Vishnu sometimes include Buddha instead of Sri Krishna or Balarama.