Short answer
Yes. Sunni Muslims believe the Prophet ﷺ will intercede on the Day of Judgement: first for all people, so the reckoning can begin, then for sinful believers of his ummah. Intercession (shafa'ah) happens only with Allah's permission and only for those He approves, so it never replaces faith and good deeds.
The intercession of the prophets, and of the Prophet ﷺ above all, for believers who committed major sins is true and part of Sunni creed, as stated in al-Fiqh al-Akbar and the Tahawi creed. Intercession for those who die in disbelief will not be accepted.
The four schools agree on this.
Explanation
The Quran sets the rule: "Who is it that can intercede with Him except by His permission?" (2:255). On that Day no intercession benefits except from one the Most Merciful permits and whose word He accepts (20:109), and only for one He approves (21:28). For the disbelievers, the intercession of intercessors will not benefit them (74:48).
Within that rule, the hadith describe several intercessions. The greatest (al-shafa'a al-uzma) comes when people stand in terrible heat and go from Adam to Nuh, Ibrahim, Musa and Isa asking for help, until they come to the Prophet ﷺ, who prostrates before Allah and is told to ask. This begins the judgement for all of humanity. He also intercedes for believers who deserve the Fire, that they not enter it or be brought out of it, and for raising the ranks of people in Jannah.
He said every prophet was given one answered prayer which he used in this world, and that he saved his for intercession for his ummah on the Day of Resurrection. He also said his intercession is for the people of major sins in his ummah. Angels, other prophets, martyrs, scholars, and even the Quran and fasting will intercede by Allah's permission.
How can you hope for it? Die on tawheed, follow his Sunnah and send salawat on him. He said whoever says the dua after the adhan, asking Allah to give him al-wasila and the praised station, will have his intercession on the Day of Resurrection. See the adhan for the dua, and Will Muslims stay in Hell forever?
The evidence
Quran, Surah Al-Baqara 2:255
ٱللَّهُ لَآ إِلَٰهَ إِلَّا هُوَ ٱلْحَىُّ ٱلْقَيُّومُ ۚ لَا تَأْخُذُهُۥ سِنَةٌۭ وَلَا نَوْمٌۭ ۚ لَّهُۥ مَا فِى ٱلسَّمَٰوَٰتِ وَمَا فِى ٱلْأَرْضِ ۗ مَن ذَا ٱلَّذِى يَشْفَعُ عِندَهُۥٓ إِلَّا بِإِذْنِهِۦ ۚ يَعْلَمُ مَا بَيْنَ أَيْدِيهِمْ وَمَا خَلْفَهُمْ ۖ وَلَا يُحِيطُونَ بِشَىْءٍۢ مِّنْ عِلْمِهِۦٓ إِلَّا بِمَا شَآءَ ۚ وَسِعَ كُرْسِيُّهُ ٱلسَّمَٰوَٰتِ وَٱلْأَرْضَ ۖ وَلَا يَـُٔودُهُۥ حِفْظُهُمَا ۚ وَهُوَ ٱلْعَلِىُّ ٱلْعَظِيمُ ﴿٢٥٥﴾
Allah - there is no deity except Him, the Ever-Living, the Sustainer of [all] existence. Neither drowsiness overtakes Him nor sleep. To Him belongs whatever is in the heavens and whatever is on the earth. Who is it that can intercede with Him except by His permission? He knows what is [presently] before them and what will be after them, and they encompass not a thing of His knowledge except for what He wills. His Kursi extends over the heavens and the earth, and their preservation tires Him not. And He is the Most High, the Most Great.
Intercession only happens with Allah's permission.
Quran, Surah Taa-Haa 20:109
يَوْمَئِذٍۢ لَّا تَنفَعُ ٱلشَّفَٰعَةُ إِلَّا مَنْ أَذِنَ لَهُ ٱلرَّحْمَٰنُ وَرَضِىَ لَهُۥ قَوْلًۭا ﴿١٠٩﴾
That Day, no intercession will benefit except [that of] one to whom the Most Merciful has given permission and has accepted his word.
Only those Allah permits may intercede.
Quran, Surah Al-Anbiyaa 21:28
يَعْلَمُ مَا بَيْنَ أَيْدِيهِمْ وَمَا خَلْفَهُمْ وَلَا يَشْفَعُونَ إِلَّا لِمَنِ ٱرْتَضَىٰ وَهُم مِّنْ خَشْيَتِهِۦ مُشْفِقُونَ ﴿٢٨﴾
He knows what is [presently] before them and what will be after them, and they cannot intercede except on behalf of one whom He approves. And they, from fear of Him, are apprehensive.
Intercession is only for those Allah approves.
Quran, Surah Al-Muddaththir 74:48
فَمَا تَنفَعُهُمْ شَفَٰعَةُ ٱلشَّٰفِعِينَ ﴿٤٨﴾
So there will not benefit them the intercession of [any] intercessors.
Intercession will not help those who die in disbelief.
Sahih al-Bukhari 335
Sahih... وَأُعْطِيتُ الشَّفَاعَةَ وَكَانَ النَّبِيُّ يُبْعَثُ إِلَى قَوْمِهِ خَاصَّةً ...
"And I have been given intercession. Every prophet before was sent to his own people only."
Intercession is one of the special gifts given to the Prophet.
Sahih Muslim 199
Sahih... لِكُلِّ نَبِيٍّ دَعْوَةٌ مُسْتَجَابَةٌ يَدْعُو بِهَا ...
"Every prophet has an answered prayer that he makes; I have saved mine as intercession for my ummah on the Day of Resurrection."
The Prophet saved his special prayer for his ummah.
Sunan Abi Dawud 4739
Graded sahih... شَفَاعَتِي لأَهْلِ الْكَبَائِرِ مِنْ أُمَّتِي ...
"My intercession is for the people of major sins in my ummah."
His intercession reaches sinful believers.
Sahih al-Bukhari 614
Sahih... حَلَّتْ لَهُ شَفَاعَتِي يَوْمَ الْقِيَامَةِ ...
"My intercession will be due to him on the Day of Resurrection."
Said of whoever recites the dua after the adhan.
Where the ruling is recorded
- al-Fiqh al-Akbar (Imam Abu Hanifa), Section on intercession. States that the intercession of the prophets, and of our Prophet, for believers with major sins is true.
- al-Aqida al-Tahawiyya, Section on intercession. Affirms the intercession the Prophet has stored for his ummah.
This answer is pending review by the scholars on our team. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.