Question
What are the exact ten avatars of Vishnu?
Answer
This isn't a proper answer, but then again I don't think there can be a proper answer. The notion of Dasavatharam isn't a notion that's found in Hindu scriptures; there are countless avatarams of Vishnu found in Hindu scriptures, such as the approximately twenty-four avatarams of Vishnu found in the Srimad Bhagavatam, and different people have made different lists of what they think the "top ten" should be. People have generally settled on the first seven: Matsya, Kurma, Varaha, Narasimha, Vamana, Parashurama, and Rama. The question is one who the last three are. The four contenders are Balarama, Krishna, Buddha, and Kalki.
Some people consider Balarama to be purely an avataram of Vishnu's serpent Adiseshan, so they say Krishna, Buddha, Kalki. Sri Vaishnavas consider Adiseshan himself to be an avataram of Vishnu, so they say Balarama, Krishna, Kalki. (And it may even be due to some skepticism about whether Buddha is an avataram at all.) Gaudiya Vaishnavas like Jayadeva give Krishna an elevated status, not viewing him as a mere avataram of Vishnu (in fact they sometimes say Vishnu is an avataram of Krishna), so they say Balarama, Buddha, Kalki. I even know of temple carvings that show Balarama, Krishna, Buddha, because they don't want to count Kalki as he is yet to come.
Who is right? It's not really possible to say one way or another, since the question of which avatarams are "most important" or "main" is pretty much a subjective matter. If you were to walk up to me on the street and ask me to rattle off the Avatarams of Vishnu I would say Matsya, Kurma, Varaha, Narasimha, Vamana, Parasurama, Rama, Balarama, Krishna, Kalki. But I'm biased, as I'm an Iyengar (a Sri Vaishnava Brahmana).
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