Sahih Muslim Book 031, Number 5955:
'A'isha reported that Allah's Apostle (may peace be upon him) went out one morning wearing a striped cloak of the black camel's hair that there came Hasan b. 'Ali. He wrapped him under it, then came Husain and he wrapped him under it along with the other one (Hasan). Then came Fatima and he took her under it, then came 'Ali and he also took him under it and then said: Allah only desires to take away any uncleanliness from you, O people of the household, and purify you (thorough purifying)
The Hadith al-Kisa' (The Hadith of the Cloak) clearly defines who the Ahl al-Bayt (A.S.) are. Ibn 'Abbas is quoted to have said:
"The Prophet of Allah (S.A.W.) spread a cloak over 'Ali, Fatimah, Hasan, and Husayn (A.S.) and recited: 'Allah only desires to keep away uncleanness from you, O people of the House! And to purify you a (thorough) purifying'. "Umm Salamah has said: "When the (aforementioned) ayah was revealed, the Prophet of Allah (S.A.W.) prayed for 'Ali, Fatimah, Hasan, and Husayn and covered them with a Khaybari cloak and said, 'My Lord, these are my Ahl al-Bayt, keep them away from uncleanness and keep them clean and pure.' "Then Umm Salamah asked the Prophet (S.A.W.): "Am I also one of them (the Ahl al-Bayt)" , to which the Prophet answered: "You are very good, but no (you are not one of the Ahl al-Bayt)."
This hadith has been quoted very widely through Umm Salamah by such people as 'Ata' bin Yasar, Abu Sa'id al-Khudri, Abu Hurayrah, Hakim bin Sa'd, Shahr bin Hawshab, 'Abdullah bin al-'Abidin. However, there is also another hadith quoted through 'Ayishah which Safiyyah bint Shaybah al-'Awam bin Hawshab and Jami' bin 'Umar have narrated through 'Ayishah, which is as follows:
"The Prophet of Allah (S.A.W.) left home early one morning, covering himself with a ... (sic) made of black wool. Then Hasan bin 'Ali arrived and went under that covering; then Husayn joined them, following which Fatimah, joined in their company; (and) then 'Ali, too, entered into the covering; then the Prophet (S.A.W.) recited: 'Allah only desires to keep away uncleanness from you, O peoplet of the House! And to purify you a (thorough) purifying."
Many of the Prophet's (S.A.W.) companions have narrated this hadith, including Abu Sa'id al-Khudri, Abu Barzah, Abu al-Hamra', Abu Ya'la Ansari, Anas bin Malik, Bara' bin 'Azib, Thawban, Jabir bin 'Abdullah Ansari, Zayd bin Arqam, Zaynab bint Abi Salamah, Sa'd bin Abi Waqqas, Sabih the retainer of Umm Salamah, 'Abdullah bin Ja'far, 'Umar bin Abi Salamah, 'Umar bin al-Khattab, as well as others, and all their narrations unanimously emphasize that the Prophet (S.A.W.) referred to "'Ali, Fatimah, Hasan, and Husayn (A.S.) as his Ahl al-Bayt". Most of the documents related to this particular hadith have been extracted from the sihah of the Ahl al-Sunnah and their encyclopedias of ahadith.