Abu Hurayrah had the best memory among the Companions of the Messenger of Allah (peace and blessings be upon him)

Abu Salih states that Sayyiduna Abu Hurayrah (may Allah be pleased with him) was among those Companions of the Messenger of Allah (peace and blessings be upon him) who memorised the most hadiths.

Abu Rafi' narrates: I heard Sayyiduna Abu Hurayrah (may Allah be pleased with him) say: "I have memorised from the hadith of the Messenger of Allah (peace and blessings be upon him) things that I have not narrated to you, and if I were to tell you even one of them, you would stone me with stones."
This hadith has an authentic (sahih) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

Sa'id bin Abi al-Hasan narrates that none of the Companions (may Allah be pleased with them) narrated more hadith than Sayyiduna Abu Hurayrah (may Allah be pleased with him). Marwan appointed him governor over Madinah and wanted (to put) his hadith (into writing), so Marwan said: "Narrate to us just as you narrated before." When he refused (to dictate them), Marwan caught him unawares and (secretly) seated a scribe for him. So Sayyiduna Abu Hurayrah (may Allah be pleased with him) kept narrating and the scribe kept writing, until all of his hadith were complete. Then Marwan said: "Do you know that we have written down all of your hadith?" He asked: "Have you really done that? If you listen to me, erase it." The narrator said: So Marwan erased it.

Abu al-Zu'ayzi'ah, the scribe of Marwan bin al-Hakam, narrates that Marwan summoned Sayyiduna Abu Hurayrah (may Allah be pleased with him) and seated me behind the throne. Marwan began asking him questions while I kept writing, until, when a year had passed, Marwan summoned him again and seated him behind a curtain, then asked him the same questions again, and he (in his answers) neither added anything nor left anything out, nor did he put any words before or after (their place).
This hadith has an authentic (sahih) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Hudhayfah (may Allah be pleased with him) that a man said to Sayyiduna Abdullah bin Umar (may Allah be pleased with them both): "Abu Hurayrah narrates a great many hadith from the Messenger of Allah (peace and blessings be upon him)." Sayyiduna Ibn Umar (may Allah be pleased with them both) said: "I seek refuge for you with Allah from falling into any doubt about what he brings (from the Prophet). The truth is that he was bold (in narrating) and we were hesitant."