Since the list of avataras are actually perfectly mentioned, I am going to provide few links and to answer the question little bit in details, will also add details on the end of the avatar.
22 Vishnu avatars in chapter 1.3
Four Kumaras (Catursana): the four Sons of god Brahma and exemplified the path of devotion
[Ending] These are believed to living still, named as Sanak, Sanandan, Sanatan, Sanat. Or commonly named as 'SanatKumaras'. They are believed to be living since almost the starting of this universe.
Reference here
Narasimha: The man-lion who kills demon Hiranyakashpu
AND
Varaha: The divine warthog who lifts earth from cosmic waters
[Ending] Varaha Avtar and his three boar sons then created mayhem in the world, which necessitated Shiva to take the form of Sharabha, to kill the Varaha form. Here, Narasimha appears to aid Varaha. Sharabha kills Narasimha first and then kills Varaha, allowing Vishnu to reabsorb the energies of both his fierce forms.
Reference here
Note: This is a view, and many of the puranas might have it written in different ways.
Narada: the divine-sage who travels the worlds as a devotee of Vishnu
[Ending] Narada, is believed to be still alive, but has stopped landing on earth. Additionally there is a story in bhagwat purana about his previous birth or past life .
Reference here
Nara-Narayana: the twin-sages
[Ending] This is more of a concept, I suppose, and they keep reincarnating.
Reference here
Kapila: a renowned sage spoken of in the Mahabharata, son of Kardama Muni and Devahuti and sometimes identified with the founder of the Samkhya school of philosophy
[Ending] not defined, but mostly not mentioned anywhere as alive after 500 BCE.
Dattatreya: the combined avatar of the Hindu trinity Brahma, Vishnu and Shiva. He was born to the sage Atri became a great seer himself.
[Ending] This avatara has reincarnated many times and as described in Shir Guru Charitra, meditated in Kardalivan (Which is located near the Jyotirlinga region of Srisailam in Andhra Pradesh, you might want to read the translated page for the link given) and later disappeared before Shri Narsimha Saraswati Avatar was born.
Yajna: the lord of fire-sacrifice, who was also a previous
[Ending] This more of a concept, than the avtar, but Vishnu himself reincarnated is what is said, and no mention of end of this avtar is mentioned anywhere. Its uncertain whether it ended, as yajna's are carried out even today.
Reference here, for details of Yajna (Not sure whether you will get the details on end of the avatara)
Indra : the lord of heaven
[Ending] Indra is actually a post, current Indra is named Purandara, as per Shirmad Bhagwat Purana, people appointed at this position usually last for the entire manvantar, and then after the dooms day, it start over again and then a new Indra is elected, based on few criteria. Reference here
Rishabha: the father of Bharata Chakravartin and Bahubali
[Ending] His death is believed in Jainism to have occurred on Ashtapada (also known as Mount Kailash) on the fourteenth day of Magha Krishna (Hindu Calendar).[54][52][55] His total age at that time is suggested to be 84 lakh purva years, with three years and eight and a half months remaining of the third ara Reference Here
Prithu: the sovereign-king who milked the earth as a cow to get the world's grain and vegetation and also invented agriculture
[Ending] After governing his kingdom for a long time, Prithu left with his wife Archi, to perform penance in the forest in his last days. He experienced Samadhi and voluntarily gave up his body in the forest, and Archi went Sati on his funeral pyre. Reference here
The Typical 10 avtaras are as below:
Rest links are pending, will be updating it soon
Matsya: A narwhal who guided Manu's ark during the pralaya (deluge) and also killed demon Hayagriva
Kurma: A giant tortoise who balances Mount Mandara atop his carapace during the churning of cosmic ocean of milk
Dhanvantari: the father of Ayurvedic medicine and a physician to the Devas
Mohini: the enchantress
Vamana: The dwarf-brahmana who takes the three worlds from Bali Maharaj and purifies Him
Parashurama: The Brahmin warrior with an axe who kills Kartyavira Arjuna and his Kshatriya allies
Sri Rama: 'Perfect King' from Suryavansha, Subject of Ramayana
Vyasa: the compiler of the scriptures – Vedas and writer of the scriptures (Puranas) and the epic Mahabharata
Balarama: Elder brother of Krishna.
Krishna: Subject of the Mahabharata and the Bhagavad Geethai
Garuda: Garuda purana
Kalki: The Divine Lawgiver
Avatars like Hayagriva, Hamsa and Garuda are also mentioned in the Pancharatra making the total of thirty-nine avatars.
However, despite these lists, the commonly accepted number of ten avatars for Vishnu was fixed well before the 10th century CE.
Madhvacharya also regards Gautama Buddha as an avatar of Vishnu.