Chiranjivis

Chiranjivis are mortals who have been blessed or cursed with an exceptionally long lifespan.They are born to accomplish extraordinary feats and will live in this world till the purpose of their birth is fulfilled.There are seven Chiranjivis mentioned in Hindu puranas and they are refered to as 'Saptha Chiranjivi' meaning 'The Seven Chiranjivis'.

HANUMAN

Hanuman is the son of Lord Vayu,the wind god.During his childhood,he once mistook the sun for a sweet fruit and reached for it.Indra,the Lord of Devas was terrified of the consequences and struck him with his Vajrayutham.This made Hanuman unconscious and he fell down.On seeing this,Lord Vayu  got very angry and he withdrew from all the creations .To please Vayu and bring back life to the Earth,all the Gods gave Hanuman multiple boons making him a Chiranjivi!

VIBISHANA

Vibishana is the righteous brother of Ravana,the demon king of Lanka.When Ravana abducted Sita,wife of Lord Rama,an avatar of Vishnu,Vibishana renounced his brother and joined Lord Rama in his battle against Ravana.Lord Rama praised Vibishana for his dharmic ways and blessed him to remain on Earth and protect Dharma by making him a Chiranjivi .

MAHABALI

Mahabali is a virtuous and powerful asura king who was tricked into giving away his kingdom by Lord Vishnu as the devas were fearful of his might.However,Lord Vishnu was deeply touched by the devotion and righteousness of King Mahabali that he granted him a boon.The king asked Vishnu to allow him to visit his people once in a year.This day is celebrated by his people as 'Onam ' in Kerala.Lord Vishnu also blessed him to live as a  Chiranjivi.

MARKENDAYA

Markendaya is a great sage and staunch devotee of Lord Shiva. His parents, Sage Mrikandu and Marudvati were childless for a long time and prayed to Lord Shiva for a child.Lord Shiva fulfilled their wish and asked them to choose between an exceptional son who would live for sixteen years or an ordinary son who would live much longer.They chose the former and thus,Markendaya was destined to die on his sixteenth birthday.

 On his sixteenth birthday,Markendaya saw his parents in deep sorrow and asked them for the reason behind their unhappiness.After much persuasion,they told him about the boon Lord Shiva had given them.Markendaya left the house and began worshipping a Shiva Linga.Lord Yama sent his messengers to take away Markendaya's life but they could not suceed as Markendaya was holding the Shiva Linga tightly.Seeing this,Lord Yama came and threw a rope around Markendaya which accidentally hit the Shiva Linga.Lord Shiva,who was deeply moved by Markendaya's devotion kicked Yama and blessed him that he will always remain sixteen,making him a Chiranjivi .

SAGE VYASA

Sage Vyasa is the son of Sage Parashara and Satyavathi .He is the foremost of Sages and is the compiler of the Holy Vedas. The great Indian Epic "Mahabaratha" was composed by Vyasa to enable us to understand the values which we have adhere to in life and is considered as the 'Fifth Veda'.He  also composed  the eighteen puranas,Brahmasutras and Bhagavatham,the story of Lord Krishna.Sage Vyasa is considered to be an avatar of Lord Vishnu and is living as a Chiranjivi.

SAGE PARASURAMA

Sage Parasurama is the son of Sage Jamadagni and Renuka.He is an avatar of Lord Vishnu,born to rid the world of unrighteous Kshatriyas.Parasurama also plays a very important role in the Mahabaratha as the Guru of Bhishma and Karna.He is a Chiranjivi and will be the martial arts Guru of Vishnu's final avatar,Kalki.

ASHWATHAMA

Aswathama is the son of son of Guru Dronacharya and Kripi.He fought alongside the Kauravas in the Kurukshetra war.Lord Krishna cursed Ashwathama to remain a Chiranjivi and suffer miserably for unleashing the Brahmastra on Uthara's womb to kill the unborn son of Abhimanyu.It is believed that he will be redeemed from this curse in the next yuga.

Sources:

http://www.hindufaqs.com/seven-immortals-chiranjivi-hindu-mythology-part-2/

https://www.quora.com/Who-are-the-seven-chiranjeevis-in-Hindu-mythology

http://www.hindudevotionalblog.com/2012/03/seven-chiranjeevis-in-hinduism.html

https://en.wikipedia.org/wiki/Vibhishana

http://www.bhagavatam-katha.com/sage-story-sage-markandeya-winning-over-death/

https://en.wikipedia.org/wiki/Bhishma