We all know about Shri Ram and Shri Krishna because of Ramayana and Mahabharat. They both are incarnations of Shri Hari Vishnu. In Shrimad Bhagvat Geeta, Shri Krishna said t o Arjun that whenever there will be too much sin on earth he (Shri Vishnu) will incarnate himself and kill all siners. So, According to Vishnu Puran, there are 10 incarnations of Shri Hari Vishnu, let's see his all incarnations.
Matsya avatar is the first incarnation of Shri Vishnu. This incarnation first killed a demon Haygriva who stolen Vedas from Brahma. Then one day, Manu was doing Tarpan near a ocean and he finds a small fish asking for help. When he put that fish in a glass its size increased and it increased so much that he had to leave that fish into ocean and after leaving it into ocean, fish again got increased in size. Then Manu knew that the fish is Shri Vishnu only who told him that destruction is going to happen. He asked him to collect all valuable items in the boat and Matsya appeared at time of Mahapralaya and took that boat to a safe place.
When there was a huge fight between Devas and Asurs, on advice of Vishnu they both agreed for churning of ocean for Amrit. Sumeru Mountain was used for churning and to rotate it Vasuki (snake on neck of Shiv) was used and Shri Vishnu took Kurma avatar for churning of ocean as something was needed on which mountain can be kept and can be rotated easily. In this Samudra Manthan, Shiv ji consumed poison and became "Neelkanth" and Amrit was consumed by devas with help of Vishnu.
A demon named Hiranyaksha stolen earth and put it in bottom of ocean and Shri Vishnu took form of a boar called Varaha avatar and he fought with him around 1000 years and killed him and brought earth between his tusks and restored it to its place in the universe.
After death of Hiranyaksa his younger brother Hiranyakashyap decided to take revenge and took boon from Brahma that no man or animal can kill him with any weapon neither in day nor in night and neither in house nor outside house and not in day and not in night and not on earth not in air. He announced in his kingdom that no one should worship Vishnu but his own son Prahlad was one of the biggest devotee of Shri Vishnu. He tried his best to kill his son but he always got failure and also lost his sister Holika and one day he tied Prahlad into a pillar and said worship you Vishnu and let me see if he can save you. He was about to kill Prahlad but Narsingh appeared from the pillar and killed Hiranaykashyap as he was half man and half lion, he killed him in evening in his lap with his nails in Chaukhat (neither inside nor outside his house).
Vishnu incarnated himself into a dwarf so that Prahlad's grandson Bali couldn't rule over whole world. Bali was doing 100th yajna so that he can become king of heaven and Shri Vishnu appeared as Vaman and asked Bali to give him land which can be measured by his 3 footsteps. Bali agreed and Vaman increased his size and covered whole universe in just 2 footsteps and asked Bali where to put 3rd step. Bali said to put his last step on his head and Vaman did the same and Bali went to Paatal and Vishnu gave him a boon to be one of the Chiranjeevis.
There was a time on Earth when Kshatriyas was dominating the world and once a king named Kartavirya Arjuna demanded Kamdhenu from sage Jambadagni but he refused and king destroyed the whole ashram and Vishnu incarnated himself as Parshuram son of sage Jambadagni and killed that king in his own place. Parshuram was student of Shiv, sons of that king killed Jambadagni and Parshuram vowed to kill every Kshatriya on the planet, he killed all kshatriyas over 21 times and filled five lakes with their blood. He gave Shiv dhanush- Pinak to king Janaka, king of Mithila. He is chiranjeevi too and it is said he lives on Mahendragiri.
Once a demon Ravan was torturing the whole world and devas too. Everyone asked help from Shri Vishnu. He took avatar as Ram in Ayodhya as son of Kaushalya and King Dashratha with 3 brothers- Bharat, Lakshaman and Shatrughan. Shri Ram and Lakshman went along sage Vishwamitra and killed demons and Ram married Sita by breaking Pinak given by Parshuram and they arrived Ayodhya and they both along with Lakshman went for 14 years of exile and Sita got kidnapped by Ravan and Shri Ram killed Ravan and his whole dynatsy except Vibhishana who was his devotee. Lord Hanuman helped Shri Ram in this war along with army of monkeys. Hanuman is also one of the chiranjeevi.
Shri Vishnu incarnated as Shri Krishna who was born inside a prison in Mathura and grew in Gokul. He killed his uncle Kans who tried to kill him after a Akashvaani that his sister's 8th child will kill him and he kept his sister and brother-in-law in prison but Shri Krishna escaped from prison due to his Maya and killed Kans and became king of Dwarka and helped Pandavs in war of Mahabharat.
Acoording to Vishnu and Bhagvat Puran, Gautam Buddha is considered as 9th incarnation of Vishnu while in South Balram is considered as 8th and Krishna as 9th incarnation. While Marathi and in Odisha people considers Vithal and Jagannath respectively as 9th incarnation. But acoording to purans Gautam Buddha is 9th avatar. Gautam Buddha was founder of Buddhism.
The 10th incarnation is yet to appear and will be seen in last stage of Kal Yuga when there will be no Dharma left in this world. According to Bhagvat Puran, Kalki avatar will be taken in Sambhala Village in Himalayas and his parents will be Vishnuyash and Sumati. He will be coming on Devdutt named horse and will kill all siners.
According to Bhagvat Puran, apart from these incarnations Shri Vishnu has other incarnations in the following sequene- Adi Purush, Four Kumars, Narad (also called mind of Vishnu), Nara Narayana, Kapila, Dattatraya(combination of Brahma, Vishnu and Mahesh), Yajna, Rishabha, Prithu, Dhanvantari, Mohini, Hayagreeva, Vyasa and these 10 incarnations. When there is a lot of sins, Shri Vishnu incarnated himself and has saved the world.
"OM NAMO BHAGVATE VASUDEVAYAH!"