There are six kinds of incarnations of Lord Sri Krishna: (1) the purusa-avatara, (2) the lila-avatara, (3) the guna-avatara, (4) the manvantara-avatara, (5) the yuga-avatara, and (6) the Saktyavesa-avatara.
Lord Sri Krishna is the svayam-rupa Personality of Godhead, and all other forms of Godhead are Lord Sri Krishna's plenary portions and integrated parts. Balarama is the first plenary manifestation of Lord Krishna. From Baladeva expands Sankarshana, Vasudeva, Pradyumna and Aniruddha. From Sankarshana there is an expansion of Narayana, and from Narayana there is a second quadruple expansion of Sankarshana, Vasudeva, Pradyumna and Aniruddha. From second Sankarshana comes Maha-Vishnu - the first purusa-avatara. Maha-Vishnu in the Causal Ocean, is the creator of the aggregate material energy. Garbhodakasayi Vishnu, is an expansion of Pradyumna; and the third purusa Ksirodakasayi Vishnu, is an expansion of Aniruddha.
i) Maha-Vishnu or Karanodakasayi avatara
These innumerable universes are produced from the pores of the Maha-Vishnu's body. As innumerable particles of dust pass through tiny holes in a screen, innumerable universes emanate from the pores of Maha-Vishnu's body. As He breathes out, innumerable universes are produced, and as He inhales, they are annihilated. All of the energies of Maha-Vishnu are spiritual, and they have nothing to do with material energy. InBrahma-samhita (5.48) it is stated that the predominating deity of each universe, Brahma, lives only during one breath of Maha-Vishnu. Thus Maha-Vishnu is the original Supersoul of all the universes and the master of all universes as well.
ii) Garbhodakasayi Vishnu
The second Vishnu incarnation, the Garbhodakasayi Vishnu, enters each and every universe, spreads water from His body, and lies down on that water. From His navel, the stem of a lotus flower grows, and on that lotus flower the first creature, Brahma, is born. Within the stem of that lotus flower are fourteen divisions of planetary systems, which are created by Brahma. Within each universe the Lord is present as the Garbhodakasayi Vishnu, and He maintains each universe and tends to its needs. Although He is within each material universe, the influence of material energy cannot touch Him. When it is required, this very same Vishnu takes the form of Lord Siva and annihilates the cosmic creation. The three secondary incarnations - Brahma, Vishnu and Siva - are the predominating deities of the three modes of material nature. The master of the universe, however, is the GarbhodakaSayi Vishnu, who is worshiped as the Hiranyagarbha Supersoul. The Vedic hymns describe Him as having thousands of heads. Although He is within the material nature, He is not touched by it.
iii) Ksirodakasayi Vishnu
The third incarnation of Vishnu, is also an incarnation of the mode of goodness. He is also the Supersoul of all living entities, and He resides on the ocean of milk within the universe.
A list of incarnations is given in Srimad-Bhagavatam (1.3), and they are as follows: (1) Kumaras, (2) Narada, (3) Varaha, (4) Matsya, (5) Yajna, (6) Nara-narayana, (7) Kardami Kapila, (8) Dattatreya, (9) Hayasirsa, (10) Hamsa, (11) Dhruvapriya or Prsnigarbha, (12) Rsabha, (13) Prthu, (14) Narasimha, (15) Kurma, (16) Dhanvantari, (17) Mohini, (18) Vamana, (19) Bhargava (Parasurama), (20) Raghavendra, (21) Vyasa, (22) Pralambari Balarama, (23) Krishna, (24) Buddha (25) Kalki.
Because almost all of these twenty-five lila-avataras appear in one day of Brahma, which is called a kalpa, they are sometimes called kalpa-avataras. Out of these, the incarnation of Hamsa and Mohini are not permanent, but Kapila, Dattatreya, Rsabha, Dhanvantari and Vyasa are five eternal forms, and they are more celebrated. The incarnations of the tortoise Kurma, the fish Matsya, Nara-narayana, Varaha, Hayasirsa, Prsnigarbha, and Balarama are considered to be incarnations of Vaibhava.
There are three guna-avataras, or incarnations of the qualitative modes of nature, and these are Brahma, Vishnu and Siva.
The Supreme Personality of Godhead, Vishnu, resides within the material world as the sattva-guna-avatara. Lord Siva is the tamo-guna-avatara, and Lord Brahma is the rajo-guna-avatara, but although Lord Vishnu is among them, He is not in the same category.
For the purpose of creation, Brahma is manifested, and for annihilation there is Lord Siva. As far as the spiritual entrance into the material world is concerned, all beings are part and parcel of the Supreme Lord, but under the covering of different material qualities they have different names. Lord Brahma and Lord Siva are qualitative incarnations of Vishnu, as guna-avataras, and Vishnu with them accepts control of the quality of goodness; therefore He is also a qualitative incarnation like Lord Siva and Lord Brahma. Actually the different names exist for different directions, otherwise the origin is one only. Lord Vishnu is deva-deva, the chief of all the demigods.
The avataras associated with the reign of each Manu, known as manvantara-avataras, are listed as follows in Srimad-Bhagavatam (Eighth Canto, chapters 1, 5 and 13): (1) Yajna, (2) Vibhu, (3) Satyasena, (4) Hari, (5) Vaikuntha, (6) Ajita, (7) Vamana, (8) Sarvabhauma, (9) Rsabha, (10) Visvaksena, (11) Dharmasetu, (12) Sudhama, (13) Yogesvara and (14) Brhadbhanu. All together these are fourteen in number, and of these, Yajna and Vamana are also counted among the lila-avataras. All thesemanvantara incarnations are sometimes called vaibhava-avataras.
The four yuga-avataras are also described in Srimad-Bhagavatam. In the Satya-yuga, the incarnation of God is white; in the Treta-yuga He is red; in the Dvapara-yuga, He is blackish; and in the Kali-yuga He is also blackish, but sometimes, in a special Kali-yuga, His color is yellowish (as in the case of Chaitanya Mahaprabhu).
The Saktyavesa-avataras are categorized into (1) forms of divine absorption (bhagavad-avesa), such as Kapiladeva and Rsabhadeva, and (2) divinely empowered forms (Saktyavesa), of whom seven are foremost: (a) Sesa Naga in the Vaikuntha world, empowered for the personal service of the Supreme Lord (sva-sevana-sakti), (b) Anantadeva, empowered to bear all the planets within the universe (bhu-dharana-sakti), (c) Lord Brahma, empowered with the energy to create the cosmic manifestation (srsti-sakti), (d) Catuhsana, or the Kumaras, specifically empowered to distribute transcendental knowledge (jnana-sakti), (e) Narada Muni, empowered to distribute devotional service (bhakti-sakti), (f) Maharaja Prthu, specifically empowered to rule and maintain the living entities (palana-sakti) and (g) Parasurama, specifically empowered to cut down rogues and demons (dusta-damana-sakti).
The expansions of different forms of the Lord are like lamps of equal power which kindle from one lamp to another. That is the transcendental potency of the Lord. The Vedas say that He is so complete that even though the whole complete identity emanates from Him, He still remains the same complete whole (purnasya purnam adaya purnam evavasisyate [ISo Invocation]). The living entities are separated parts and parcels of the Personality of Godhead. Therefore Lord Sri Krishna is the original form of Godhead, and He is the last word in the Transcendence. Thus He is more attractive to the higher transcendentalists who participate in the eternal pastimes of the Lord. In forms of the Personality of Godhead other than Sri Krishna and Baladeva, there is no facility for intimate personal contact as in the transcendental pastimes of the Lord at Vrajabhumi.
There is no end to the expansions and incarnations of Krishna. It is confirmed in Srimad-Bhagavatam(1.3.26) that there is no limit to the incarnations of the Supreme Lord, just as there is no limit to the waves of the ocean.