Dasavatar

1. Matsya, the fish, appeared in the Satya Yuga.The Fish Incarnation is the first incarnation of Vishnu. Lord Vishnu takes the form of a fish in order to retrieve the Vedas from the demon Hayagriva, who stole them from Lord Brahma. Without the Vedas, Creation of the Universe cannot take place. He slayed the demon Hayagriva, recovered the Vedas, and also saved the pious king Satyavrata from the deluge so that life and religion can be preserved for the next cycle of Creation.
2. Kurma, the tortoise, appeared in the Satya Yuga. The turtle Incarnation is the second incarnation of Vishnu. When the devas and asuras were churning the ocean in order to get the nectar of immortality, the mount Mandara they were using as the churning staff started to sink and Lord Vishnu took the form of a turtle to bear the weight of the mountain.
3. Varaha, the boar, appeared in the Satya Yuga. The Boar incarnation is the third incarnation of Vishnu. He appeared in order to defeat Hiranyaksha, a demon who had taken the Earth (Prithvi) and carried it to the bottom of what is described as the cosmic ocean in the story. The battle between Varaha and Hiranyaksha is believed to have lasted for a thousand years, which the former finally won. Varaha carried the Earth out of the ocean between his tusks and restored it to its place in the universe.
4. Narasimha, the half-man/half-lion appeared in the Satya Yuga. The Man-Lion Incarnation is the fourth incarnation of Vishnu. When the demon Hiranyakashipu acquired a boon from Brahma, which gave him inordinate power, Lord Vishnu appeared in the form of half-man/half-lion, having a human-like torso and a lower body, but with a lion-like face and claws. Hiranyakashipu could not be killed by human, deva or animal, Narasimha is neither one of these, as he is a form of Vishnu incarnate as a part-human, part animal. He comes upon Hiranyakashipu at twilight (when it is neither day nor night) on the threshold of a courtyard (neither indoors nor out), and puts the demon on his thighs (neither earth nor space). Using his sharp nails (neither animate nor inanimate) as weapons, he disembowels and kills the demon.
5. Vamana, the dwarf, appeared in the Treta Yuga. The fourth lineal descendant of Hiranyakashyap, named Bali, through his devotion and penance defeated Indra, the god of firmament, humbled other gods and extended his authority over the three worlds. All the gods appealed to Lord Vishnu for protection and He became manifest in His Dwarf Avatar of Vaman for the purpose of restraining Bali. Once when this king was making a great religious offering, Lord Vishnu in the form of Vaman appeared before him in the company of other Brahmins. Bali was extremely pleased to see a holy man with such a diminutive form and promised to give him whatever he should ask. Lord Vishnu asked only for as much land as he could measure by three steps. Bali laughingly agreed to grant the boon of three steps. Lord Vishnu as dwarf stepped over heaven in first stride and earth in the second stride. Then out of respect to Bali's kindness and his grandfather Prahlad's great virtues, Lord Vishnu stopped short and left him in pathal, the subterranean region. Bali is believed to have ruled Kerala.
6. Parashurama, Rama with the axe, appeared in the Treta Yuga. Parashurama a Brahmin, the sixth avatar of Vishnu, belongs to the Treta yuga, and is the son of Jamadagni and Renuka. Parashu means axe, hence his name literally means Rama-of-the-axe. He received an axe after undertaking a terrible penance to please Shiva, from whom he learned the methods of warfare and other skills. Parashurama is said to be a "Brahma-Kshatriya" (with the duties between a Brahmana and a Kshatriya), the first warrior saint. His mother is descended from the Kshatriya Suryavanshi clan that ruled Ayodhya and Lord Rama also belonged to. A haihaya King Kartavirya Arjuna (Sahasrarjuna - purportedly with a thousand arms) and his army visited Jamadagni, a Brahmin sage, who fed his guest and the whole army with his divine cow Kamadhenu. The king demanded the magical cow. Jamadagni refused because he needed the cow for his religious ceremonies. King Kartavirya Arjuna (Sahasrarjuna) took the cow forcibly and devastated the ashram. Angered at this, Parashurama killed the king's entire army and, after cutting each one of his thousand arms, the king himself with his axe. As a revenge, the King's sons killed Jamadagni in Parashurama's absence. Furious at his father's murder, Parashurama killed all sons of Sahasrajuna and their aides. His thirst for revenge unquenched, he went on killing every adult Kshatriya on earth, not once but 21 times, filling five ponds with blood. These are the actions which highlight his warrior characteristics. Ultimately, his grandfather, Richeek Rishi, appeared and stopped him.
7. Rama, Ramachandra, the prince and king of Ayodhya, appeared in the Treta Yuga. Lord Rama is one of the most commonly adored gods in Hinduism and is known as an ideal man and hero of the epic Ramayana. Lord Rama defeated and killed the king of Sri Lanka, Ravana for capturing and imprisoning his wife Sita in the Ashoka Garden in Sri Lanka.
8. Krishna (meaning 'dark coloured' or 'all attractive') appeared in the Dwapara Yuga along with his brother Balarama. According to the Bhagavata Purana Balarama is said to have appeared in the Dwapara Yuga (along with Krishna) as an incarnation of Ananta Shesha. He is also counted as an avatar of Vishnu by the majority of Vaishnava movements and is included as the ninth Dasavatara in some versions of the list which contain no reference to Buddha. Because of his great Godly power, Lord Krishna is another of the most commonly worshipped deities in the Hindu faith. He is considered to be the eighth avatar of Lord Vishnu. He played a huge role in the Battle of Kurukshetra and helped the Pandavas defeat the Kauravas. He is also a significant character in the epic of Mahabharata. Shree Krishna delivered Bhagwad Gita on battlefield of the Battle of Kurukshetra to Arjun. He, like Lord Rama, is also known for his bravery in destroying evil powers throughout his life. The Lord is usually depicted as playing the flute (murali), indicating spread of the melody of love to people.
9. Buddha (See alternative lists below for Balarama at this position) See also: Buddha as an Avatar of Vishnu. With the departure of Lord Krishna (Krishna Avatar), the age of Kali set in, in this age, the true devotion to Vedas was replaced by empty rituals. To enlighten the world in such times, Lord Vishnu descended the earth as Buddha, the enlightened one.
10. Kalki ("Eternity", or "time", or "The Destroyer of foulness"), who is expected to appear at the end of Kali Yuga, the time period in which we currently live. The tenth and the last avatar of Vishnu, Kalki, is yet to appear. Kalki will appear at the end of the Kalyuga. This avatar will appear seated on a white horse with a drawn sword blazing like a comet. He shall come finally to destroy the wicked, to restart the new creation and to restore the purity of conduct in people's lives.