1. Matsya – fish Avatar. This avatar was taken to save the seventh Manu (Man) from perishing from universal disaster.
2. Kurma – tortoise Avatar. During the Samudra manthan, to save the earth from drowning.
3. Varaha – the boar Avatar. The demon Hiranayksha had dragged the earth down to the sea and so to save the earth, with the horns, the Varaha brough the earth back to surface
4. Narsimha – Man-lion Avatar. This avatar was taken to kill the demon Hiranyakashipu whose son Prahlad was a devotee of Vishnu
5. Vaman – the dwarf Avatar. Mahabali, the demon controlled the earth, heaven and hell. The Gods lost the powers. Vishnu asked for three steps when Bali sacrificed and told Vaman to ask for boon. Vaman took heaven and earth in two steps and last step, took Patal, putting his foot on head of Bali, covering the whole Patal
6. Parshuram – The sixth avatar to bring end of evil Kshatriyas.
7. Ram – The symbol of human perfection who obeyed his father and went to forest for fourteen years with wife Sita and brother Laxman. There is a series of incidents and finally Ravana was killed who had captured Sita.
8. Krishna – the Kanaiya. Vishnu took birth to destroy Kansa. Krishna also played a crucial role in Mahabharata. The death of Krishna marked beginning of Kali Yuga.
9. Buddha – the enlightenment. Hinduism accepts this 9th Avatar of Buddha, Siddharth as incarnation of Vishnu. To preserve Vedas, reject caste system and deities and for meditation, peace and unity.
10. Kalki, the rider – This Avatar is yet to appear which will ride on a white horse with flaming sword and destroy all evil on earth. After the end of Kali Yuga, again there will come the Treta Yuga and so, says the Hindu Puranas.
Whether one believes or not but one can conclude that the Kali Yug is on – with the endless poverty, corruption, violence, education flaws, changing lifestyles, Internet mania and so on. One can only hope for a Ramrajya where there is no wants and wars but peace on earth.