The hadith of the pond of Khumm (Arabic: حدیث غدیر خم) has multiple versions, and a multitude of interpretations based on these different versions. The Sunni view is that the hadith is not an indication, implicitly or explicitly, of successorship, regardless of its authenticity. The answer below is solely from a Sunni point of view.
Background information
The story of the hadith is that the Prophet ﷺ appointed 'Ali ibn Abi Talib as the head of the army that he sent to Yemen. 'Ali appointed another person as the head of the army and returned to Mecca to catch up with the hajj and the Prophet ﷺ. 'Ali then revoked some of the orders that his appointee had put in place (e.g., using the camels donated as charity, taking back some of the war spoils the companions were given, etc.). The companions took this stance from 'Ali to be too harsh, and disagreements erupted. When the Prophet ﷺ finished the hajj, at Khumm, he lectured the companions to tell them that 'Ali ibn Abi Talib was correct in what he had done, to show the stance that 'Ali had among other Muslims, and to clear up the disagreements.
Authenticity of the hadith of the pond of Khumm
The hadith of the pond of Khumm was documented in many books of hadith, too many to document all (Al-Hafidh Ibn 'Uqda compiled a book about this hadith in specific, including its many versions). The conclusion is that there is a difference among scholars about the authenticity of certain parts of the hadith ("For whomever I am his Mawla then 'Ali is his Mawla"), and an agreement about the authenticity of other parts ("You are in the same position with relation to me as Harun was in relation to Moosa but with the explicit difference that there is no prophet after me"), as well as an agreement about the lack of authenticity of other parts ("O' Allah, take as friends those who take him as a friend, and take as enemies those who take him as an enemy").
In Jami' Al-Tirmidhi, we have two versions:
حَدَّثَنَا مُحَمَّدُ بْنُ بَشَّارٍ، حَدَّثَنَا مُحَمَّدُ بْنُ جَعْفَرٍ، حَدَّثَنَا شُعْبَةُ، عَنْ سَلَمَةَ بْنِ كُهَيْلٍ، قَالَ سَمِعْتُ أَبَا الطُّفَيْلِ يُحَدِّثُ عَنْ أَبِي سَرِيْحَةَ أَوْ زَيْدِ بْنِ أَرْقَمَ ـ شَكَّ شُعْبَةُ ـ عَنِ النَّبِيِّ ﷺ قَالَ
مَنْ كُنْتُ مَوْلاَهُ فَعَلِيٌّ مَوْلاَهُ
قَالَ أَبُو عِيسَى هَذَا حَدِيثٌ حَسَنٌ صَحِيحٌ غَرِيبٌ. وَقَدْ رَوَى شُعْبَةُ هَذَا الْحَدِيثَ عَنْ مَيْمُونٍ أَبِي عَبْدِ اللَّهِ عَنْ زَيْدِ بْنِ أَرْقَمَ عَنِ النَّبِيِّ ﷺ. وَأَبُو سَرِيحَةَ هُوَ حُذَيْفَةُ بْنُ أَسِيدٍ الْغِفَارِيُّ صَاحِبُ النَّبِيِّ ﷺ
Narrated Abu Sarihah, or Zaid bin Arqam — Shu'bah had doubt — from the Prophet (ﷺ):
For whomever I am his Mawla then 'Ali is his Mawla.
— Jami' Al-Tirmidhi 49/4078
The second version is in Jami' Al-Tirmidhi 49/4077.
In addition, the hadith was documented by Ibn Majah in his Sunnan through a different chain of narration:
حَدَّثَنَا عَلِيُّ بْنُ مُحَمَّدٍ، حَدَّثَنَا أَبُو مُعَاوِيَةَ، حَدَّثَنَا مُوسَى بْنُ مُسْلِمٍ، عَنِ ابْنِ سَابِطٍ، ـ وَهُوَ عَبْدُ الرَّحْمَنِ ـ عَنْ سَعْدِ بْنِ أَبِي وَقَّاصٍ، قَالَ قَدِمَ مُعَاوِيَةُ فِي بَعْضِ حَجَّاتِهِ فَدَخَلَ عَلَيْهِ سَعْدٌ فَذَكَرُوا عَلِيًّا فَنَالَ مِنْهُ فَغَضِبَ سَعْدٌ وَقَالَ تَقُولُ هَذَا لِرَجُلٍ سَمِعْتُ رَسُولَ اللَّهِ ﷺ يَقُولُ
مَنْ كُنْتُ مَوْلاَهُ فَعَلِيٌّ مَوْلاَهُ
وَسَمِعْتُهُ يَقُولُ
أَنْتَ مِنِّي بِمَنْزِلَةِ هَارُونَ مِنْ مُوسَى إِلاَّ أَنَّهُ لاَ نَبِيَّ بَعْدِي
وَسَمِعْتُهُ يَقُولُ
لأُعْطِيَنَّ الرَّايَةَ الْيَوْمَ رَجُلاً يُحِبُّ اللَّهَ وَرَسُولَهُ
It was narrated that Sa'd bin Waqqas said: "Mu'awiyah came on one of his pilgrimages and Sa'd entered upon him. They mentioned 'Ali, and Mu'awiyah criticized him. Sa'd became angry and said: Are you saying this of a man of whom I heard the Messenger of Allah (ﷺ) say:
If I am a person's close friend, 'Ali is also his close friend.
And I heard him say:
You are to me like Harun was to Musa, except that there will be no Prophet after me.
And I heard him say:
I will give the banner today to a man who loves Allah and His Messenger.
— Sunan Ibn Majah 1/126
The second version is in Sunan Ibn Majah 1/121.
It is the view of some scholars that the portion "For whomever I am his Mawla then 'Ali is his Mawla" (Arabic: مَنْ كُنْتُ مَوْلاَهُ فَعَلِيٌّ مَوْلاَهُ) is a later addition to the hadith (e.g., Ibn Taymiyyah in Minhaj Al-Sunna, Arabic:
منهاج السنة النبوية في نقض كلام الشيعة القدرية). The scholars who do not accept the authenticity of this version base this on the multiple hadiths quoted in Sahih Al-Bukhari (62/57, and 64/438) and Sahih Mulsim (44/47, 44/48, 44/50, and 44/51) that do not have this addition.
Some other scholars (e.g., Al-Mubarakpuri in Sharh Jami' Al-Tirmidhi, Arabic: تحفة الاحوذي بشرح جامع الترمذي) are of the opinion that the hadith in its entirety has other good chains that strengthen the argument of its authenticity. Ibn Hajar shared a similar view in several of his books.
Other scholars (e.g., Al-Albani in Al-Silsila Al-Sahiha, Arabic: سلسلة الأحاديث الصحيحة) said the hadith was authentic, with the first part being mutawatir (the portion mentioned in Sahih Al-Bukhari and Sahih Muslim).
Sunni view on the Prophet ﷺ choosing 'Ali to be his successor
There is a consensus among Sunni scholars, including the ones that authenticate the hadith, that the interpretation of the hadith does not indicate that the Prophet ﷺ chose 'Ali ibn Abi Talib as his successor.
Al-Bayhaqi in his book Al-I'tiqad (Arabic: الاعتقاد والهداية إلى سبيل الرشاد على مذهب السلف وأصحاب الحديث) said:
وأما حديث الموالاة فليس فيه ـ إن صح إسناده ـ نص على ولاية علي بعده، فقد ذكرنا من طرقه في كتاب الفضائل ما دلّ على مقصود النبي ﷺ من ذلك، وهو أنه لما بعثه إلى اليمن كثرت الشكاة عنه وأظهروا بغضه فأراد النبي ﷺ أن يذكر اختصاصه به ومحبته إياه ويحثهم بذلك على محبته وموالاته وترك معاداته فقال
من كنت وليه فعلي وليه
وفي بعض الروايات
من كنت مولاه فعلي مولاه، اللهم وال من والاه وعاد من عاداه
والمراد به: ولاء الإسلام ومودته، وعلى المسلمين أن يوالي بعضهم بعضا ولا يعادي بعضهم بعضا
— NOTE: My own translation, so treat with care:
As the hadith of muwalah — if it is authentic — does not stipulate that 'Ali succeeds the Prophet ﷺ, for we have explained in the book of virtues (Al-Fada'el) what the Prophet ﷺ intended by saing so. When he appointed him to go to Yemen, there were many complaints. The Prophet ﷺ wanted to show the special stance that he ['Ali] has, the Prophet's love for him, and to urge them to love him and support him and abandon any hatred they may have had toward him ['Ali]. The Prophet ﷺ said:
For whomever I am his Mawla then 'Ali is his Mawla.
And in some narrations:
O' Allah, take as friends those who take him as a friend, and take as enemies those who take him as an enemy
What is meant here is the muwalah of Islam, and associated love, as is required from all Muslims to have muwalah to other Muslims, and to drop any enmity.
The word mawla means worth of love and support. For instance, in this verse, Allah ﷻ uses the word mawlah:
إِن تَتُوبَا إِلَى اللَّهِ فَقَدْ صَغَتْ قُلُوبُكُمَا ۖ وَإِن تَظَاهَرَا عَلَيْهِ فَإِنَّ اللَّهَ هُوَ مَوْلَاهُ وَجِبْرِيلُ وَصَالِحُ الْمُؤْمِنِينَ ۖ وَالْمَلَائِكَةُ بَعْدَ ذَٰلِكَ ظَهِيرٌ
If you two [wives] repent to Allah, [it is best], for your hearts have deviated. But if you cooperate against him — then indeed Allah is his protector, and Gabriel and the righteous of the believers and the angels, moreover, are [his] assistants.
— Qur'an 64:4
It is evident that the verse means if the Prophet's two wives go against the Prophet ﷺ that Allah and Gabriel and all the believers will extend their protection, love, and support to the Prophet ﷺ, not rule the Prophet ﷺ.
Also, in this verse, Allah ﷻ is talking about Al-Muhajereen:
إِنَّ الَّذِينَ آمَنُوا وَهَاجَرُوا وَجَاهَدُوا بِأَمْوَالِهِمْ وَأَنفُسِهِمْ فِي سَبِيلِ اللَّهِ وَالَّذِينَ آوَوا وَّنَصَرُوا أُولَٰئِكَ بَعْضُهُمْ أَوْلِيَاءُ بَعْضٍ ۚ وَالَّذِينَ آمَنُوا وَلَمْ يُهَاجِرُوا مَا لَكُم مِّن وَلَايَتِهِم مِّن شَيْءٍ حَتَّىٰ يُهَاجِرُوا ۚ وَإِنِ اسْتَنصَرُوكُمْ فِي الدِّينِ فَعَلَيْكُمُ النَّصْرُ إِلَّا عَلَىٰ قَوْمٍ بَيْنَكُمْ وَبَيْنَهُم مِّيثَاقٌ ۗ وَاللَّهُ بِمَا تَعْمَلُونَ بَصِيرٌ
Indeed, those who have believed and emigrated and fought with their wealth and lives in the cause of Allah and those who gave shelter and aided — they are allies of one another. But those who believed and did not emigrate — for you there is no guardianship of them until they emigrate. And if they seek help of you for the religion, then you must help, except against a people between yourselves and whom is a treaty. And Allah is Seeing of what you do.
— Qur'an 8:72
Here again the verse is talking about guardianship, and not about the Muslims all ruling other Muslims. There are several other verses in Qur'an and hadiths that talk about muwalah that show the word does not automatically mean successorship.
The virtues of 'Ali ibn Abi Talib
The Sunni view holds 'Ali ibn Abi Talib to the highest stance among the companions. He is the fourth among the ten companions told to be from the dwellers of Jannah while still alive (Jami' at-Tirmidhi 49/4112), the fourth of Al-Khulafa' Al-Rashedeen (Sunan Ibn Majah 1/45) that we are ordered to follow their sunnah, etc. If we were to attempt to compile all the virtues of 'Ali ibn Abi Talib, which was tried by Ibn Hanbal and Al-Nasa'i and others, the task would almost prove impossible. Moreover, 'Ali ibn Abi Talib was the first boy to embrace Islam, the one who was willing to sacrifice his life for the sake of the Prophet ﷺ on the night of Hijra, and above all, he is from Ahl Al-Bayt (the close relations of the Prophet ﷺ), and the husband of the Prophet's daughter Fatima. The Prophet ﷺ had often praised the people Ahl Al-Bayt, in general (e.g., when he said "I have left among you, that which if you hold fast to it, you shall not go astray: The Book of Allah and my family, the people of my house" in Jami' at-Tirmidhi 49/4155), and 'Ali in specific (e.g., when he told 'Ali "You are from me, and I am from you" in Sahih Al-Bukhari 64/286).
It is important to understand that albeit the Sunni view is that the successorship was not specified to 'Ali, that he is and will always be revered by Sunnis in the highest stance.
