Dashavathara of Sriman Narayana

(Source: http://en.wikipedia.org/wiki/Dashavatara_of_Vishnu) In Sri Vaishnava philosophy, an avatar (अवतार, avatāra), most commonly refers to the incarnation and dasa refers to ten in number. They are:
  1. Matsya, the fish, appeared in the Satya Yuga.
  2. Kurma, the tortoise, appeared in the Satya Yuga.
  3. Varaha, the boar, appeared in the Satya Yuga.
  4. Narasimha, the half-man/half-lion appeared in the Satya Yuga.
  5. Vamana, the dwarf, appeared in the Treta Yuga.
  6. Parashurama, Rama with the axe, appeared in the Treta Yuga.
  7. Rama, Ramachandra, the prince and king of Ayodhya, appeared in the Treta Yuga.
  8. Balarama (according to the Bhagavata Purana) is said to have appeared in the Dwapara Yuga (along with Krishna) as an incarnation of Ananta Shesha
  9. Krishna (meaning 'dark coloured' or 'all attractive') appeared in the Dwapara Yuga along with his brother Balarama.
  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 exist, which will end in the year 428899 CE.

Goutama Buddha is considered WRONGLY in Dasavataras now-a-days. Note that some people mistakenly assume Goutama Buddha to be an incarnaton of Sriman Narayana. They also quote Namm Azhwar to have portrayed Vanamamalai Perumal as having taken the avatara of Buddha in one of his pasurams. It's rather unfortunate if you ask me - born out of ignorant enthusiasm - considering that Buddhism is a flawed philosophy. You will realize this if you read the clear and logical arguments put forth by Sri Bhagvad Ramanujacharya in his mangum-philosophical-opus called Sri Bhashyam against among other philosophies, Buddhism. It was a primary reason for Buddhism's natural death in India.

Note: The BEST SOURCE TO READ FOR UNDERSTANDING OUR CULTURAL DEPTH IS THE VISHNU PURANA. It talks about the Yugas, Brahma’s Age, Manus and a lot more.