When the Prophet (peace and blessings be upon him) was angry, no one dared speak to him except Ali (may Allah be pleased with him)

It is narrated from the Mother of the Believers, Sayyidah Umm Salamah (may Allah be pleased with her), that when the Prophet (peace and blessings be upon him) was in a state of majestic displeasure (anger), none of us except Sayyiduna Ali bin Abi Talib (may Allah be pleased with him) had the courage to speak to him (peace and blessings be upon him).
This hadith has a sahih (authentic) chain of narration, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Abu Uthman al-Nahdi that a man said to Sayyiduna Salman al-Farisi (may Allah be pleased with him): "How intensely you love Ali!" He replied: "I heard the Messenger of Allah (peace and blessings be upon him) say: 'Whoever loves Ali has loved me, and whoever hates Ali has hated me.'"
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it.

It is narrated from Sayyiduna Buraydah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings be upon him) said: "Indeed, Allah Almighty has commanded me to love four people from among my Companions, and He has informed me that He (Allah) also loves them." We said: O Messenger of Allah! Who are they? Each of us wished that we were among them. He (peace and blessings be upon him) said: "Behold! Ali is one of them." Then he (peace and blessings be upon him) fell silent, and then said again: "Surely Ali is one of them."
This hadith is sahih (authentic) on the condition of Imam Muslim, but the two Shaykhs (Bukhari and Muslim) did not record it.

It is narrated from Sayyiduna Anas bin Malik (may Allah be pleased with him) that he said: I used to serve the Messenger of Allah (peace and blessings be upon him). Once a roasted bird was presented before the Messenger of Allah (peace and blessings be upon him), and he (peace and blessings be upon him) supplicated: "O Allah! Send to me the one among Your creation who is most beloved to You, so that he may eat this bird with me." Sayyiduna Anas (may Allah be pleased with him) says: I prayed (within myself): O Allah! Let that person be someone from the Ansar. Just then Sayyiduna Ali (may Allah be pleased with him) came, and I said: The Messenger of Allah (peace and blessings be upon him) is occupied with some need (task). He came again, and I again said: The Messenger of Allah (peace and blessings be upon him) is occupied with some need. When he came (the third time), the Messenger of Allah (peace and blessings be upon him) said: "Open the door." So he entered, and he (peace and blessings be upon him) asked: "What kept you from coming to me?" He said: This was the last, the third time, that Anas turned me back, saying that you were occupied with some task. The Messenger of Allah (peace and blessings be upon him) asked (Anas (may Allah be pleased with him)): "What prompted you to act this way?" I said: O Messenger of Allah! I had heard your supplication, so I wished that the fortunate person would be someone from my own people (the Ansar). The Messenger of Allah (peace and blessings be upon him) said: "Indeed, a person loves his own people."
This hadith is sahih (authentic) on the condition of the two Shaykhs (Bukhari and Muslim), but they did not record it. It has been narrated from Sayyiduna Anas (may Allah be pleased with him) by a group of his students numbering more than thirty; moreover, in support of it there are also sahih narrations from Sayyiduna Ali, Sayyiduna Abu Sa'id al-Khudri and Sayyiduna Safinah (may Allah be pleased with them).

It is narrated from Thabit al-Bunani that Sayyiduna Anas bin Malik (may Allah be pleased with him) was ill, and Muhammad bin al-Hajjaj came with some of his companions to visit him. During the conversation there, Sayyiduna Ali (may Allah be pleased with him) was mentioned, and Muhammad bin al-Hajjaj disparaged him. At this Sayyiduna Anas (may Allah be pleased with him) said: "Who is this? Sit me up." When he had been sat up, he said: "O Ibn al-Hajjaj! Do I see you speaking disparagingly of Ali bin Abi Talib? By the One who sent Muhammad (peace and blessings be upon him) with the truth, I used to serve the Messenger of Allah (peace and blessings be upon him) in his presence, and every day a young man from among the sons of the Ansar would attend to serve him (peace and blessings be upon him); that day was my turn. Umm Ayman, the freed slave-woman of the Messenger of Allah (peace and blessings be upon him), brought a bird and placed it before him (peace and blessings be upon him). The Messenger of Allah (peace and blessings be upon him) asked: 'O Umm Ayman! What is this bird?' She said that this was a bird she had obtained and prepared for him. The Messenger of Allah (peace and blessings be upon him) supplicated: 'O Allah! Send to me the one among Your creation who is most beloved to You and to me, so that he may eat this bird with me.' Meanwhile there was a knock at the door, and the Messenger of Allah (peace and blessings be upon him) said: 'O Anas! See who is at the door.' I prayed (within myself): O Allah! Make him a man from the Ansar. I went, and there was Sayyiduna Ali (may Allah be pleased with him). I said (to put him off) that the Messenger of Allah (peace and blessings be upon him) was occupied with some task, and then I came back and stood in my place. Only a little while had passed when there was another knock, and he (peace and blessings be upon him) said: 'O Anas! See who is at the door.' Again I wished: O Allah! Make him a man from the Ansar. I went, and again it was Sayyiduna Ali (may Allah be pleased with him). I again said the same, that the Messenger of Allah (peace and blessings be upon him) was busy, and came back to my place. After a little while there was another knock, and the Messenger of Allah (peace and blessings be upon him) said: 'O Anas! Go and bring him in. You are not the first person to have loved his own people. He is not from the Ansar.' So I went and brought him in, and he (peace and blessings be upon him) said: 'O Anas! Bring the bird close to him.'" The narrator says: I placed the bird before him (peace and blessings be upon him), and the two of them ate it together. Muhammad bin al-Hajjaj asked (in amazement): "O Anas! Did all this happen in your presence?" He replied: "Yes." So Muhammad bin al-Hajjaj said: "I make a firm covenant with Allah that from today I will never disparage Ali, nor will I hear anyone speak ill of him without answering him sternly."