Normally the Daśāvataras or 10 incarnations of Viṣṇu starting with Matsya are famous. But various Purāṇas give different lists of 22 or more. The following is the list from Garuḍa Purāna and a small brief of their significance

The avatāras of incarnations of Śrī Hari or Śrī Viṣṇu is innumerable, but various Purāṇas list different number of important incarnations. Following are 22 avataras mentioned in Garuḍa Purāna Purva Khanḍa, Chapter 1. Mentioned in brackets are my comments.

1. Kumaras (Sanat Kumārās) – in first Sarga, they did Akhanda Brahmacharya or unbroken restraint of their senses including being celibate.

2. Śukara (Varaha), Yajñeśa – in second Sarga, He went to Rasatala and uplifted the submerged earth. Anupādati means to enter. So Sri Hari entered the form of a boar or Shukara

3. Devaṛsi (Nārada) – in third Sarga. Propounded the Sātvata Tantra which explicates upon Nishkāma karma.

4. Nara-Nārāyaṇa – in fourth Sarga. For protection of Dharma, they did rigorous tapa (austerities) and they were worshipped by both Suras and Asuras

5. Kapila – Lord of the Siddhas, ended the ruin of Dharma by Kali (yuga) by teaching the Surās, the Sankhya way to have a precise understanding of all Tattvās

6. Dattātreya – son of Atri through Anasuya. Explained to Prahlada and others and to Alarka the Ānvikshika vidya. (Refer: https://www.wisdomlib.org/definition/anvikshiki)

7. Yajña – son of Ruchi Prajāpati and Ākuti in Svayambhuva manvantara. He conducted and completed and Yajna with his minister (Amātya) – Satya and with all the Suras.

8. Urukrama – son of Meru Devi and king Nābhi. He propounded the philosophy (darsana) of Sarvāśrama Namaskṛta which is an excellent discipline. (The eighth incarnation was King Rishabha, son of King Nabhi and his wife Merudevi. In this incarnation the Lord showed the path of perfection, which is followed by those who have fully controlled their senses and who are honored by all orders of life.)

9. Pṛthu – Appeared due to the solicitation by the Rishis. By milking medicinal herbs from the earth and others which rejuvenated the lives of all the people

10. Matsya – appeared during the Mahapralaya or Great Deluge in Cāksusa Manvantara. He protected Vaivasvata Manu by placing him on a boat

11. Kamaṭha (kUrma) – For the Samudra Manthana (Churning of the Ocean) by Suras and Asuras, He appeared as Kurma and bore the Mandarachala mountain on His back

12. Dhanvantari – (The Divine Physician who appeared with the Amrta Kalasha)

13. Mohini – to strengthen (āpyāyata) the Devas (by ensuring they get the Amṛta and not the Asuras)

14. Narasimha – Killed the arrogant daitya Hiranyakasipu, by ripping him apart

15. Vāmana – By begging for three steps He conquered entire three worlds and banished king Bali

16. (Parasurāma) – Witnessing the persecution of Brahmanas by the Kshatriyas, he destroyed them so that the world was without Kshatriyas – 3x7 i.e. 21 times. (Its interesting that the way the number 21 has been depicted here as being 3 times 7)

17. (Vedavyāsa) – Son of Parāsara through Satyavati, He divided the Vedas into different shākhas for the less intelligent men of the age

18. (Rāma) – incarnating as king of men, he accomplished the tasks of Suras like controlling or supressing the ocean and other feats (interestingly the key feat of Rama of destroying Ravana is not mentioned, rather the bridging of the sea is considered more important)

19. Rāma (Balarāma)

20. Kṛṣṇa – In the 19th and 20th avataras, by incarnating as Rāma and Krsna, the removed the heavy burden on earth giving her relief (of the asuras who had incarnated as kings and their population flourishing)

21. Budha – appearing at the Sandhya of Kali Yuga, as son of Jina, in KeekaTa (Magadha?) to bewildering the enemies of the Suras

22. Kalki – in the 8th Sandhya of Kali, when the kings are destroyed (i.e. when there will be anarchy), He will come as son of Viṣṇuyaśa.