The most famous of the divine incarnations are Rama, whose life is depicted in the Ramayana, and Krishna, whose life is depicted in the Mahabharata and the Bhagavata Purana. The Bhagavad Gita, which contains the spiritual teachings of Krishna, is one of the most widely read scriptures in Hinduism. Mohini is a female incarnation of Vishnu who appeared during the early struggle between the Deva and Asura.
Matsya : the fish, appeared in the Satya Yuga. Represents the beginning of life.
Kurma : the tortoise, appeared in the Satya Yuga. Represents a human embryo just growing tiny legs, with a huge belly.
Varaha : the boar,appeared in the Satya Yuga. Represents a human embryo which is almost ready. Its features are visible.
Narasimha : the Man-Lion (Nara = man, simha = lion), appeared in the Satya Yuga. Represents a newborn baby, hairy and cranky, bawling and full of blood. Regarded as the greatest and most powerful avatar.
Vamana : the Dwarf, appeared in the Treta Yuga. Represents a young child.
Parashurama : Rama with the axe, appeared in the Treta Yuga. Represents both an angry young man and a grumpy old man simultaneously.
Rama : Sri Ramachandra, the prince and king of Ayodhya, appeared in the Treta Yuga. Represents a married man with children and depicts an ideal society. one man one wife etc..,. Lord Rama is considered Purna avatar, which means full incarnation of Vishnu.
Krishna : Krishna is considered Purna avatar, which means full incarnation of Vishnu. Represents a more realistic society. As chaotic as it looks there is clear demarcation between right and wrong.
Balarama : the older brother of Krishna, also known as Baladeva.
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 exist, though it has not happened yet. However, over the centuries many sects have believed their spiritual leader to be Kalki. For example, Ismaili Khojas, a Muslim group from Gujarat and Sindh who are followers of Aga khan, believe in the 10 incarnations of Vishnu. (Source : Wiki)