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I know that there are many avatars of Vishnu but some say that the famous Dashavatar include lord Buddha (Wiki) and some say as Balarama (hinduism.about.com). but Mohini avatar is not considered as part of Ten avatars.
What are the exact famous Dasavatarms as mentioned in Scriptures?
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).
Bhrigu rishi cursed Vishnu to take repeated births on earth (Devi Bhagavata, 4.12.8,9) for which He is taking innumerable incarnations here and we are having a problem to decide what are the exact dashaavataras.
When scriptures describe the avatars of Vishnu, which are infinite, they include both Balarama and Buddha as Vishnu's incarnations. For example, Shrimad Bhagavatam says as below:
In the nineteenth and twentieth incarnations, the Lord advented Himself as Lord Balarāma and Lord Kṛṣṇa in the family of Vṛṣṇi and by so doing He removed the burden of the world. [SB - 1.3.23]
Then, in the beginning of Kali-yuga, the Lord will appear as Lord Buddha, the son of Añjanā, in the province of Gayā, just for the purpose of deluding those who are envious of the faithful theist. [SB - 1.3.24]
So also, Garuda Puran mentions both Balarama and Buddha as an incarnations of Vishnu:
ekonaviṃśe viṃśatime vṛṣṇiṣu prāpya janmanī
rāmakṛṣṇāviti bhuvo bhagavānaharadbharam
tataḥ kalestu sandhyānte sammohāya suradviṣām
buddho nāmrā jinasutaḥ kīkaṭeṣu bhaviṣyati [Grd. Pur- 1.1.31,32]In brief: 20th,21st are Rama-Krishna born in the Vrshni clan. Then in Kali, He will become Buddha in Kikata (modern Gaya province).
But wherever a list of ten is given, most of the times Buddha replaces Balarama. For example:
dharma saṃrakṣaṇārthāya adharmādivinaṣṭaye
daityarākṣasanāśārthaṃ matsyaḥ pūrvaṃ yathābhavat
kūrmo varāho nṛharirvāmano rāma ūrjitaḥ
yathā dāśarathī rāmaḥ kṛṣṇobuddho'tha kalki api [Grd, Pu. - 1.86.10,11]
Then in the 3.15 chapter, Garuda puran gives a list of incarnations where Buddha is prsent but not Balarama.
Similarly, the Varaha Puran lists the ten incarnations with Buddha as below:
matsyaḥ kūrmo varāhaśca narasiṃho'tha vāmanaḥ
rāmo rāmaśca kṛṣṇaśca buddhaḥ kalkī ca te daśa [Vrh. Pu. - 4.2]Mastya, Kurma, Varaha, Narasimha, Vamana, Parshurama, Rama, Krishna, Buddha, Kalki are the ten incarnations.
Similarly, the Agni Puran goes on to describe the ten avatars one by one and in the list it describes about Buddha as one of them in the 16th chapter. Even the Vishnu Puran (3.17.41) mentions Buddha as in incarnation of Vishnu.
But does this means Buddha exactly belongs to the Dashavatara? Probably not. It just means, Buddha certainly belongs to the popular Dashavatara list. It's because some scriptures even neither mention Buddha nor Balarama in their list of ten incarnations. For example, the Vayu Puran replaces them with Dattatreya and Vedavyasa. Then one verse whose origin I don't know mentions Balarama but not Buddha:
matsyaḥ kūrmo varāhaśca narasiṃhaśca vāmanaḥ
rāmo rāmaśca rāmaśca kṛṣṇaḥ kalkirjanārdanaḥ
- The ten incarnations are: Mastya, Kurma, Varaha, Narasimha, Vamana, Parshurama, Rama, Balarama, Krishna,and Kalki.
So moral of the story? Many scriptures mention Buddha in the ten avatars and some don't. So Buddha belongs to the popular list of ten incarnations of Vishnu. But because Buddha spread a non-Vedic tenet, some people do not accept Him as an incarnation of Vishnu and replace Him with Balarama. But if you go by the scriptures, then both are incarnations of Vishnu. So chose whoever you like and include Him in your list of dashavataras. At the end of the day, His incarnations are nothing but infinite:
avatārā hyasaṃkhyeyā hareḥ [Grd. Puran - 1.1.34 / SB - 1.3.26]
हरि अनंत हरिकथा अनंता [RCM - 1.139]
Supreme lord's reincarnations may not be predictable. They might be happening all the time at many places without our knowledge.
During MahAbhArata ShAnti Parva, few of the important reincarnations are described:
Endued with four forms, I shall, in this way, achieve many feats of great prowess, and attain at last to those regions of felicity created by me and honoured by all the Brahmanas. Appearing in the forms of a
1. swan,
2. a tortoise,
3. a fish,
O foremost of regenerate ones, I shall then display myself as
4. a boar,
5. then as a Man-lion (Nrisingha),
6. then as a dwarf,
7. then as Rama of Bhrigu's race,
8. then as Rama, the son of Dasaratha,
9. then as Krishna the scion of the Sattwata race,
10. and lastly as Kalki.
When the auditions in the Vedas disappeared from the world, I brought them back.
Please refer to Jayadeva Goswami's Dasavataram stotra here
The ten avatars described are:
There is also a list of the 22 scheduled incarnations of Lord Visnu in the Srimad Bhagavatam 1.3
Those are described as the four Kumaras, Varaha, Narada, Nara and Narayana Rsi, Kapila, Dattatreya, Yajna, Rsabhadeva, Prthu, Matsya, Kurma, Dhanvantari, Mohini, Nrsimha, Vamana, Parasurama, Vyasadeva, Balarama, Krishna, Buddha, and Kalki.
You can see there is some overlap between them but the Srimad Bhagavatam gives a more comprehensive list.
Although Purans do not explicitly mention Dash Avatar, but we can deduce it commonly.. Akrura prays to the incarnations of Lord inside Yamuna river (famously known as Akrura Dashavatar stuti ) when he sees the past and future incarnations of Lord there.. He prays to major 10 incarnations also adding Lord Hayagriva. He calls the form Vasudeva, Sankarshana, Pradyumna and Aniruddha as the form of Lord of Satvas [ ie. Lord Krishna ]. I think the concept of 10 Avatar came from here as the Purans do not focus so much about Lord Hayagriva...
Bhagwat Puran
१०४००१७१ नमः कारणमत्स्याय प्रलयाब्धिचराय च १०४००१७३ हयशीष्णे नमस्तुभ्यं मधुकैटभमृत्यवे १०४००१८१ अकू पाराय बृहते नमाे मन्दरधारिणे १०४००१८३ क्षित्युद्धारविहाराय नमः शूकरमूर्तये १०४००१९१ नमस्तेऽद्भूतसिंहाय साधुलाेकभयापह १०४००१९३ वामनाय नमस्तुभ्यं क्रान्तत्रिभुवनाय च १०४००२०१ नमाे भृगुणां पतये द्दप्तक्षत्रवनच्छिदे १०४००२०३ नमस्ते रघुवर्याय रावणान्तकराय च १०४००२११ नमस्ते वासुदेवाय नमः सड़्करषणाय च १०४००२१३ प्रद्युन्मयनिरूद्धाय सात्वतां पतये नमः १०४००२२१ नमाे बुद्धाय शुद्धाय दैत्यदानवमाेहिने १०४००२२३ म्लेच्छप्रायक्षत्रहन्ते नमस्ते कल्किरूपिणे
17-18. I offer my obeisances to You, the cause of the creation, Lord Matsya, who swam about in the
ocean of dissolution, to Lord Hayagriva, > the killer of Madhu and Kaitabha, to the immense tortoise, [Lord
Kurma] , who supported Mandara Mountain, and to the boar incarnation [Lord Varaha], who enjoyed
lifting the earth.
19. Obeisances to You, the amazing lion [Lord Nrisimha] , who remove Your saintly devotees’ fear, and
to the dwarf Vamana , who stepped over the three worlds.
20. Obeisances to You, Lord of the Bhrgus [Lord Parashurama] , who cut down the forest of the conceited royal order, and to
the best of the Raghu dynasty, Lord Rama , who put an end to the demon Ravana.
21. Obeisances to You, Lord of the Satvatas [Lord Krishna] , and to Your forms of Vasudeva, Sankarsana, Pradyumna
and Aniruddha.
22. Obeisances to Your form as the faultless Lord Buddha , who will bewilder the Daityas and Danavas,
and to Lord Kalki, the annihilator of the meat-eaters posing as kings. >
Also Agam doctrines support this 10 Avatar associating with 10 Maha Vidyas of Tantra.
As many pointed out, there are many views of the composition of the list. Hence it depends on whom you would like to follow to have the meaning of your word exact in your question.
If I were you, I would follow vaishnava philosophy and Swami Sri Desikan is considered as authority (though there are branches which do not follow his principles, no one disagrees with the contribution that he has done). As per that swamy who composed dasaavathara stotram. This stotram enumerates the dasaavatar as:
The 4000 divya prabandam is composed on 12 Azhwars whose time span was before Swami Desikan (and may be before the Buddha period) says:
மீனோ டாமை கேழலரி குறளாய் முன்னு மிராமனாய்த் தானாய் பின்னு மிராமனாய்த் தாமோ தரனாய்க் கற்கியும் ஆனான் றன்னை கண்ணபுரத் தடியேன் கலிய னொலிசெய்த தேனா ரின்சொல் தமிழ்மாலை செப்பப் பாவம் நில்லாவே.
Its explanation and translation given in DravidaVeda.org says:
This nectar-sweet garland of Tamil songs by devotee kaliyan is on the Lord of kannapuram who appeared as fish, a furtile, a boar, a manlion, manikin, parasurama, Kodandarama, Balarama, krishna, and who will come as kalki too. Those who master it will be rid of evil karmas. I believe the word furtile is a typographical error for the word turtile
DashAvtAra is like a top 10 list in some puraNas.
In rAmAyana and mahAbhArata, 20+ avatAras of vishNu are mentioned like kapila, hayagrIva, prithu, hamsa, nar-nArAyaN-hari-krushNa, dattAtreya, dhanvantri, etc. Even shesha is considered a partial incarnation of vishNu in itihAsa, vishNu purAna and bhagavata purAna .
Puranas describe many incarnations of Vishnu, Shiva and Devi. As the question is on incarnations of Vishnu, I will restrict my answer to this aspect only.
After reading about Vedic Literature in Internet (I am not a sanskrit scholar), Valmiki Ramayana (It is the only authoritative text on Ramayana), Mahabharata and Puranas, I concluded that the following might be the order in which the literature came into existence.
(1) Vedic Literature (Only 3 vedas please - Atharvana veda is an addition at a later date) , (2) Srimad Ramayana (3) Mahabharata (4) Puranas. Till Mahabharata period, i.e., around 3102 B.C., the Puranas were not written and Vedic Pantheon were used to be adored.
In Vedic Era, Lord Brahma was Lord of all Lokas, (Lokadhipati), and the Ultimate boon giver, Indra's place is next to him (Lord of Devatas - Devesam) and Vayu, Agni, Varuna, Vishnu, etc are among 33 Gods we have. Vishnu's definitely used to assist Indra and Gods occasionally, but not did not have the status of God of Gods.
Sri Rama was described as the incarnation of Vishnu in Puranas and in the PRAKSHIPTA episode in Srimad Ramayana. However, Srimad Ramayana did not mention about earlier incarnations of Vishnu, except Vamana and Parasurama, which were discussed below.
1) It was PRAJAPATI - Satapatha Brahmana, who took the form of BIG fish, and saved the King, when a great deluge took place. In the later Purana's version, Vishnu was attributed with this act.
2) Srimad Ramayana clearly says (Ayodhya Kanda) that it was Lord Brahma, who took the form of VARAHA and brought out EARTH from Water.
सर्वम् सलिलम् एव आसीत् पृथिवी यत्र निर्मिता | ततः समभवद् ब्रह्मा स्वयम्भूर् दैवतैः सह || २-११०-३
"All was water only in the beginning" from which element the earth was formed. After that, the self-existent Brahma with all the gods came into existence."
स वराहः ततो भूत्वा प्रोज्जहार वसुंधराम् | असृजच् च जगत् सर्वम् सह पुत्रैः कृत आत्मभिः || २-११०-४
"Thereafter, that Brahma, assuming the form of boar, caused the earth to rise from water and with his sons of pure soul, created the entire world."
3) Kurma - turtle - Avatar was mentioned in Srimad Ramayana. However, those Sargas are not in conformity with Sage Valmiki's style because Shiva and Vishnu were described in those Sargas as GOD of Gods, which was not Valmiki's style.
4) Hiranyakasipu was mentioned in Srimad Ramayana, but Nrishimha Avatar was not mentioned.
न चापि मम हस्तात्त्वां प्राप्तुमर्हति राघवः || ५-२०-२८ हिरण्यकशिपुः कीर्तिमिन्द्रहस्तगतामिव |
"Like Keerthi got by Hiranyakasipu from Indra's hand, Rama is not suited to get you from my hands."
5) Srimad Ramayana describes Vishnu taking the form of dwarf Vamana - not an incarnation (2) He restored the wealth of Indra on one occasion.
6) According to Puranas, Parasurama was the 6th incarnation of Lord Vishnu. He makes a brief appearance in Srimad Ramayana in penultimate Sargas of Bala Kanda.
His story, in his own words, as described in those penultimate Sargas of Bala Kanda of Srimad Ramayana is as follows:
Vishnu handed over a supreme bow to Sage Riciika, the son of Bhrigu, as a trustworthy trust. That great-resplendent Sage Riciika on his part has handed over this divine bow to his son with unmatchable deeds of religious merit, who is my father Sage Jamadagni.
Adhering to a barbarous mentality Kaartvaviirya Arjuna put my father to death, when the ascetically powerful father of mine has isolated himself from arsenal.
On hearing the unregenerate and highly perfidious murdering of my father, I rancorously extirpated Kshatriya-s as and when they are born, that too not for one time, going around the earth... and on getting the entire earth under my control I performed Vedic-ritual, and at the end of that Vedic-ritual, I gave all that earth to sage Kashyapa, a sage with divine soul and with pious observances, as a ritualistic-generosity... and I am at present on Mt. Mahendra practising ascesis and thus conjoined are the powers of ascesis in me.
On hearing about the breakage of Shiva's longbow, then I promptly came here. Thereby, oh, Rama, wield this supernatural and superlative longbow of Vishnu, which is passed on to me from my forefathers and my father. Keep your fealty to Kshatriya-hood in view, and wield this as you have wielded Shiva's longbow”
The Story of Parasurama also appears in Mahabharata, wherein it was mentioned that Drona obtained all his divine weapons from the former.
Drona heard that the illustrious Brahmana Jamadagnya, Rama the son of Jamadagni, had expressed a desire of giving away all his wealth to Brahmanas. Having heard of Rama's knowledge of arms and of his celestial weapons also, Drona, who set his heart upon them as also upon the knowledge of morality that Rama possessed, set out for the Mahendra mountains.
Arrived at Mahendra, Drona approached Rama the son of Jamadagni, worshipped Rama's feet, and told him that he came there with the desire of obtaining his wealth.'
On hearing him, Rama said that he gave away his gold and whatever other wealth he had to Brahmanas! He further stated that the earth also, to the verge of the sea, decked with towns and cities, as with a garland of flowers, was given unto Kasyapa. And, he added that he was left with his body only and his various valuable weapons and that he was prepared to give either his body or his weapons.
Drona prayed to give him all his weapons together with the mysteries of hurling and recalling them and Rama gave all his weapons to Drona,
If we study these 2 stories in depth, we will find 2 contradictions.
1) If the Parasu Rama the son of Jamadagni extirpated Kshatriya-s many times by going around the earth, then lineage of both Ikshvaku's, to which Dasaratha belonged, and Nimi's, to which Janaka belonged to, must have been broken, as Parasu Rama might have eliminated Kshatriya-s of both lineages.
However, while describing the lineages of Ikshvaku's and Nimi's during the marriage ceremony of Sri Rama and Sita, Sage Valmiki did not mention about breakage of those lineages due to Parasu Rama's adventures.
2) In Mahabharata it was mentioned that Drona obtained all his divine weapons from Parasu Rama.
Mahabharata followed Srimad Ramayana, as mention about Sri Rama can be found in Mahabharata but not about Pandavas in Srimad Ramayana.
So if Parasu Rama distributed all his riches along with entire land on earth to Kashyapa and retired to Mt. Mahendra for practising ascesis, how can he still wait for Drona of Mahabharata era for imparting knowledge in divine weapons and then retire to Mt. Mahendra?
The answer is clear.
Parasu Rama existed only in Mahabharata era but not in Srimad Ramayana era. Some scholars might have inserted at a latter date the story of Parasu Rama confronting Sri Rama, the son of Dasaratha, in Srimad Ramayana to make believe the readers that Rama the son of Jamadagni was holder of Supreme Vaishnava Bow and he was infact the incarnation of Lord Vishnu that came before Sri Rama.
Hence, we can conclude that Parasu Rama was not the incarnation of Lord Vishnu.
7) Sri Rama is not an incarnation of Vishnu. It was discussed at Did King Dasaratha think of performing Putrakamesthi to beget sons, apart from Aswamedha Yagna?
8) Except in Puranas and Sri Bhagavatam, Mahabharata did not say that Sri Krishna was an incarnation of Vishnu.
