The men and women Companions known as the memorizers of Qur’an (al-qurra’) were:

1-4. The Four Rightly-Guided Caliphs. However, Abu Bakr and `Umar died before memorizing it completely, while `Uthman and `Ali were among those who gathered (jama`a) the Qur’an in the time of the Prophet — Allah bless and greet him. `Uthman was one of those who used to recite the entire Qur’an in one day and night.

5. `Abd Allah ibn Mas`ud — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

6. Salim, Mawla Abi Hudhayfa — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

7. Mu`adh ibn Jabal — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

8. Ubay ibn Ka`b — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him. He would recite it all in eight days.

9. Zayd ibn Thabit — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

10. Abu Zayd — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

11. Abu al-Darda’ — Allah be well-pleased with him– one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him. His class in the mosque of Damascus counted 1,600 students, each ten with one monitor. If a student made a mistake the monitor corrected him, and if the monitor made a mistake Abu al-Darda’ corrected him.

12. Abu Musa al-Ash`ari — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

13. `Abd Allah ibn `Amr ibn al-`As — Allah be well-pleased with him. He was ordered by the Prophet — Allah bless and greet him — to recite it in no less than seven days.

14. Talha ibn `Ubayd Allah — Allah be well-pleased with him.

15. Sa`d ibn Abi Waqqas — Allah be well-pleased with him.

16. Hudhayfa ibn al-Yaman — Allah be well-pleased with him.

17. Abu Hurayra — Allah be well-pleased with him. He was examined by Ubay.

18. `Abd Allah ibn al-Sa’ib — Allah be well-pleased with him. He was examined by Ubay.

19. `Abd Allah ibn `Umar — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

20. `Abd Allah ibn `Abbas — Allah be well-pleased with him. He was examined by Ubay.

21. `Abd Allah ibn al-Zubayr — Allah be well-pleased with him.

22. `A’isha bint Abi Bakr — Allah be well-pleased with her.

23. Hafsa bint `Umar — Allah be well-pleased with her.

24. Umm Salama — Allah be well-pleased with her.

25. `Ubada ibn al-Samit — Allah be well-pleased with him.

26. Mu`adh Abu Halima — Allah be well-pleased with him.

27. Mujammi` ibn Jariya — Allah be well-pleased with him.

28. Fadala ibn `Ubayd — Allah be well-pleased with him.

29. Maslama ibn Mukhallad — Allah be well-pleased with him.

30. Anas ibn Malik — Allah be well-pleased with him.

31. Umm Waraqa bint `Abd Allah ibn al-Harith — Allah be well-pleased with her.

32. Abu Umama al-Bahili — Allah be well-pleased with him.

33. `Utba ibn `Amir — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him.

34. Tamim al-Dari — Allah be well-pleased with him — one of those who gathered the Qur’an in the time of the Prophet — Allah bless and greet him — and who used to recite the entire Qur’an in one day and night.

When the above are added to the seventy Ansar who were killed in the battle of Yamama against Musaylima the Arch-Liar, and who were all memorizers of the Qur’an (qurra’) [Bukhari and Muslim], the number of the Companions who had memorized the Qur’an rises to over a hundred. This number excludes the numerous Companions — whether named or unnamed — whose status of memorizers did not reach us through isnad, as well as the women of both the Muhajirin and the Ansar. All of this memorizing was mass-transmitted. The numbers of the next generations, of course, keep rising exponentially in identical fashion of transmission, and praise belongs to Allah.

Sources:

1. al-Nawawi, al-Tibyan fi Adab Hamala al-Qur’an (p. 31);

2. al-Dhahabi, Tabaqat al-Qurra’ (1:24-50)

3. al-Suyuti, al-Itqan fi `Ulum al-Qur’an (1:70-72);

4. al-Zarkashi, al-Burhan fi `Ulum al-Qur’an (1:241-243);

5. Nur al-Din `Itr, `Ulum al-Qur’an al-Karim (p. 164-166).

Extracted from: http://companionofquran.wordpress.com/2009/09/15/companions-memorizers-of-quran/