1) ADI PURUSH AVATAR
(Incarnation as the Pre-eminent man) : Lord Vishnu took his first incarnation as the pre-eminent man,
with a desire to commence creation. This first incarnation of Lord Vishnu was
full of all the sixteen Kalas (Supernatural powers).
Lord Brahma manifested from the navel of Lord Vishnu in his (Lord Vishnu) state
of Yoganidra (deep meditation). The creation as well as the expansion of the
creation commenced from the organs of Lord Brahma. The first incarnation of
Lord Vishnu is all-powerful, which can be seen only by the yogins and sages who
have attained divine knowledge. This incarnation is also the indestructible
seed from which all the other incarnations manifest themselves. During the time
of final annihilation of the world, every creation merges into him.
2) THE ETERNAL YOUTHS : Sanatkumar was the 'Manasputra' (born by a wish) of Lord Brahma.
Throughout his life, he maintained celibacy; and engaged himself in the
performance of tremendous penance. He was the one from whom the Brahmins got
the inspiration regarding the values and importance of penance and Celibacy.
3) VARAHA AVATAR (The
incarnation as a Boar) : Lord Vishnu took his third incarnation as a boar. In this
incarnation Lord Vishnu rescued the earth which had submerged in the ocean, and
brought it out from the ocean. The whole creation started only after that. A
demon by the name of Hiranyaksha had abducted the earth and carried it to the
'Rasatala' (the second lowest of the world). The earth is considered to be as a
'Woman' and since it is a crime to abduct a woman therefore Lord Vishnu in his
incarnation of a boar killed the demon Hiranyaksha and liberated the earth from
his clutches.

4)
NARADA AVATAR (The incarnation as Sage Narada) : Lord Vishnu
took his fourth incarnation as Narada. Narada by becoming a
'Devarishi' among all the sages, achieved liberation from all of his Karma's
(action). Narada was the one who gave discourses to the Vaishnavas
(followers of Lord Vishnu) on 'Pancharatra Tantra'.
Lord Vishnu in his incarnation as Narada, showed that,
the devotion is the best mean of getting liberated from all the bondages of
'Karma's'. He also said that a devotee of Lord Vishnu is the supreme among the
devotees in the same way as Devarishi Narada among the Sages.
5) NARA-NARAYANA AVATAR (Incarnation as Nara-Narayana) :
Lord
Vishnu took his fifth incarnation as sage Nara-Narayan by taking a birth from
the womb of a woman named 'Kala'. He performed a tremendous penance by going to
Badri and Kedar. He showed the importance Penance (Labour), and also that
nothing can be achieved in this world without it.

6) KAPILA AVATAR(Incarnation as Sage Kapila) : Lord Vishnu's Sixth
incarnation was as sage Kapila. The objective of this incarnation was to
compile all the divine knowledge that had been destroyed. He was the profounder
of Sankhya Shastra (rationalism) which helped the Brahmins, who had forgotten
their duties to rectify their mistakes. He also gave discourse to his own
mother.

7) DATTATRAYA AVATAR
(Incarnation as Dattatraya) :
Lord
Vishnu's Seventh incarnation was as Dattatraya. He was born to Ansuya and his
father was Sage Atri. He was the one who had given Spiritual Knowledge to King
Alarka and Prahlada. He had twenty four teachers. He believed that in the
world, a man can learn from each and every thing, so he accepted twenty-four objects
like water, bird, air, an unmarried girl, and even a prostitute etc.
8) YAGYA AVATAR (Incarnation
as Yagya): Lord Vishnu in his eighth incarnation as Yagya was born to
Prajapati and Akuti. He had rescued a 'Devagana' (celestial and supernatural
being) named Yama and also the Manvantar named as 'Swayambhuva'. The main
thrust of his teaching was based on the values of helpfulness and protecting
each other during the time of crisis.

9) RISHABH AVATAR (Incarnation as Rishabh Dev) : Lord Vishnu in his ninth incarnation as Rishabh Dev was born to king Nabhi and
Marudevi. His mother Marudevi was the daughter of Indra. He attained that state
of Paramhansa (an ascetic of highest order who has controlled his anger) which
is an uphill task. He was given the title of 'Jin' which means a ' a knower'. His followers are known as Jains.
10) PRITHU AVATAR
(Incarnation as Prithu) : Lord Vishnu in his tenth incarnation as 'Prithu' came into
existence after the body of King 'Vena'. Lord Vishnu took this incarnation as
per the wishes of the sages. The earth had concealed all the vegetation's
within her and as a result the whole land had become barren. To protect the
humanity, Lord Vishnu took incarnation as Prithu by milking the cow (earth).
This is considered that as a very supreme incarnation, because the earth has
remained full of vegetation's after that.
11) MATSYA AVATAR
(Incarnation as a Fish) : All the oceans had unified into a single ocean in the
'Manvantara' of 'Chakshusha'. Lord Vishnu in his 11th incarnation as a Matsya
(Fish) rescued the earth from 'Maya' the demon. He gave discourses to Satyavrat
along with the seven sages, while they were sitting on the boat. He also showed
them his illusionary powers. This was his eleventh incarnation.

12) KACHCHAP AVATAR
(Incarnation as a Tortoise) : Lord Vishnu in his twelfth incarnation as a tortoise, held the
mountain 'Mandarachala' on his back, during the time when the deities and the
demons where churning the ocean. He stopped the mountain from going to the
netherworld. This was Lord Vishnu's twelfth incarnation.
13) DHANVANTARI (Incarnation
as Dhanvantari) :
Lord
Vishnu took his thirteenth incarnation as Dhanvantari. He manifested from the
ocean holding a vessel filled with ambrosia. He was the profounder of medicinal
science.
14) MOHINI AVATAR
(Incarnation as a most Enchanting woman) : Lord Vishnu in his fourteenth
incarnation as a most enchanting
woman enchanted the demons by his beautiful
appearance of a woman, and took away the pot filled up with ambrosia from them
and gave it to the deities. The deities were thus protected from the demons.
15) NARSIMHA AVATAR
(Incarnation in the form of half-man and half-lion) :
Lord
Vishnu took his fifteenth incarnation as Nrisimha, having upper portion of his
body in the form of lion and the lower portion resembling of a man. In this
incarnation he protected Prahlada from his father Hiranyakashipu the demon. He
killed Hiranyakashipu by tearing his body apart by his nails. Lord Vishnu had
to attain this form because Lord Brahma had blessed Hiranyakashipu, that a
Human being could not kill him.

16) HAYAGREEVA AVATAR
(Incarnation as Hayagreeva) :
Once
Lord Brahma becoming tired of his creative activities, wanted to rest. The
night of the Brahma was approaching. Because of his tiredness Lord Brahma
yawned. All the four Vedas came out from his opened mouth. A demon who used to
live near him in disguise, abducted the Vedas. Lord Vishnu took his sixteenth
incarnation as Hayagreeva to protect the Vedas. In this incarnation his face
resembled that of a horse and the rest of his body resembled that of Sri
Narayan with all of his four hands. He killed the demon and protected the
Vedas.
17) VAMAN AVATAR (Incarnation
as a Dwarf) :
Lord
Vishnu took his seventeenth incarnation as a Dwarf, when
To help the deities regain control over the heaven. Lord Vishnu disguised as a
dwarf went to
18) PARSHURAM AVATAR
(Incarnation as Parshurama) : When the Kshatriya kings became ruthless and started exploiting
their subjects. Lord Vishnu took his eighteenth incarnation as Parshurama' and annihilated
the Kshatriyas kings for seventeen times and consequently donated the earth to
the Brahmins.

19) VYAS AVATAR (Incarnation
as Sage Vyas) : Lord Vishnu took his
nineteenth incarnation as Sage Vyasa by taking birth from the womb of 'Satyavati'.
His father was sage Parashar. He made the division of Veda, and made extension
of its branches. He also wrote eighteen Mahapuranas and the Mahabharata.

20) RAM AVATAR (Incarnation as Lord Rama) : Lord Rama is
considered to be the twentieth incarnation of Lord Vishnu. In this incarnation
he constructed a bridge over the ocean with the help of the Vanars (monkeys)
and after crossing over to Lankas killed many demons like Ravana, Kumbhakarna.
He accomplished many astonishing feats and saved the deities. He taught the
value of morality.
21) BALARAM AVATAR
(Incarnation as Balrama) : Balrama is considered to be
the twenty-first incarnation of Lord Vishnu. In this incarnation he killed
Pralambasura the demon and he killed many more demons.

22)
23) BUDDHA AVATAR (Incarnation as Buddha) :
The
twenty-third incarnation of Lord Vishnu was as Lord Buddha. In the Kaliyuga the
demons were completely subjugated by the deities. Shukracharya the teacher of the
demons instigated the demons to perform Yagya so that they could regain power
and authority. Fearing this the deities prayed to Lord
Vishnu for help. Lord Vishnu took incarnation as Buddha and dissuaded the
demons from performing Yagya as it involves violence the demons stopped
performing Yagyas.
24) KALKI AVATAR (Incarnation
as Kalki) : At the end of Kaliyuga, when the sins would be 80, all pervading
that the kings would themselves becomes thieves then Lord Vishnu would take his
twenty-fourth incarnation as Kalki by taking birth in the village of
'Shambhal'. He would take birth in a Brahmin family of Vishnuyash. By killing
and destroying the sinners, he would re-establish the superiority of Virtuosity
and religiousness.
Reference: http://www.urday.com/24avtaar6.htm