The eighteen Purāṇas are divided into three groups of six by their primary deity-focus and their dominant Guṇa (quality): the six Vaiṣṇava Purāṇas (Tāmasika Purāṇas in Śaṅkara's classification, which is actually an inverse classification — they are Sāttvika): Viṣṇu, Bhāgavata, Nārada, Garuḍa, Padma, Varāha. The six Śaiva Purāṇas: Śiva, Liṅga, Skanda, Agni, Vāyu, Matsya. The six Brahma Purāṇas: Brahma, Brahmāṇḍa, Brahmavaivarta, Mārkāṇḍeya, Bhaviṣya, Vāmana. Note: the threefold classification by dominant deity is more useful than the traditional Sattva/Rajas/Tamas classification, which is itself a polemical device used by each tradition to rank its own scripture first.
The most important single Purāṇa is the Bhāgavata Purāṇa (also Śrīmad Bhāgavatam) — twelve books, approximately 18,000 verses, and the foundational scripture of the Vaishnava Bhakti tradition. Its tenth book (the Kṛṣṇa book) is the most widely read, recited, and commented upon section of any Purāṇa. The second most important for the tradition's practical life is the Śiva Purāṇa (for Shaivism) and the Devī Bhāgavata Purāṇa (for Śāktism — though its Mahāpurāṇa status is disputed in favour of the Devī Māhātmya within the Mārkaṇḍeya Purāṇa). Source: Rocher (1986).
The Bhāgavata Purāṇa — the fifth Veda of Bhakti
The Bhāgavata Purāṇa (c.900–1000 CE, South India, in its final form) is sometimes called the fifth Veda — its status in the Vaishnava tradition is essentially equivalent to the śruti (revealed scripture). Its opening verse — dharmaḥ projjhita-kaitavo 'tra paramo nirmatsarāṇāṃ satāṃ / vedyaṃ vāstavam atra vastu śivadaṃ tāpa-trayonmūlanam — declares it the text that uproots all three sources of suffering (ādhibhautika, ādhidaivika, ādhyātmika) and reveals the ultimate reality for those who are completely honest. The first nine books provide a vast theological and cosmological context; the tenth book is the Kṛṣṇa biography; the eleventh contains the Uddhava Gīta (often called the second Bhagavad Gīta — Kṛṣṇa's final teaching before his departure); the twelfth concludes with the promise of the Kali Yuga and the appearance of Kalki. Source: Bryant (2002).
The complete list — Aṣṭādaśa Mahāpurāṇa
The eighteen Mahāpurāṇas in the canonical list (with approximate verse counts and primary focus):
1. Brahma Purāṇa (~10,000 vv.) — Oḍiśā sacred geography. 2. Padma Purāṇa (~55,000 vv.) — the largest Purāṇa; Vaiṣṇava. 3. Viṣṇu Purāṇa (~23,000 vv.) — the most systematic; Viṣṇu's cosmic functions. 4. Śiva Purāṇa (~24,000 vv.) — Śiva's mythology and worship. 5. Bhāgavata Purāṇa (~18,000 vv.) — the Kṛṣṇa Purāṇa; the fifth Veda of Bhakti. 6. Nārada Purāṇa (~25,000 vv.) — the Nārada Pañcarātra. 7. Mārkāṇḍeya Purāṇa (~9,000 vv.) — contains the Devī Māhātmya. 8. Agni Purāṇa (~15,000 vv.) — encyclopaedic. 9. Bhaviṣya Purāṇa (~14,500 vv.) — prophetic. 10. Brahma Vaivarta Purāṇa (~18,000 vv.) — Rādhā-Kṛṣṇa. 11. Liṅga Purāṇa (~11,000 vv.) — Śiva-Liṅga cosmology. 12. Varāha Purāṇa (~24,000 vv.) — Viṣṇu (Varāha Avatāra). 13. Skanda Purāṇa (~81,000 vv.) — the largest Purāṇa; Skanda/Kārttikeya + Kāśī Khaṇḍa. 14. Vāmana Purāṇa (~10,000 vv.) — Viṣṇu (Vāmana Avatāra). 15. Kūrma Purāṇa (~17,000 vv.) — Viṣṇu (Kūrma Avatāra). 16. Matsya Purāṇa (~14,000 vv.) — Viṣṇu (Matsya Avatāra); contains temple-building rules. 17. Garuḍa Purāṇa (~19,000 vv.) — Viṣṇu; death rites and after-death states. 18. Brahmāṇḍa Purāṇa (~12,000 vv.) — cosmology; contains the Lalitā Sahasranāma. Source: Rocher (1986).
Rocher (1986). Bryant (2002). Coburn (1988).
The Purāṇas and the transmission of tradition to all of society
Ludo Rocher's The Purāṇas (Harrassowitz, 1986) — the definitive scholarly survey — argues that the Purāṇas represent the tradition's most sophisticated mechanism for transmitting knowledge across the full social spectrum. The Vedas were (in principle) restricted to the twice-born; the Purāṇas were explicitly open to all — women, Śūdras, and members of all communities. The Bhāgavata Purāṇa states (BhP 1.4.25): the Purāṇas were compiled specifically because Vedic knowledge was not accessible to those excluded from Vedic study. The Purāṇic tradition is thus the tradition's solution to the question of how to make liberation-knowledge universally available — through story, image, myth, and ritual rather than through the technical apparatus of Vedic learning. The result is that most of what ordinary Hindus know about their tradition comes primarily from the Purāṇas rather than from the Vedas or Upaniṣads directly. Source: Rocher (1986).