Narrated Ibn `Abbas:
I used to recognize the completion of the prayer of the Prophet (ﷺ) by hearing Takbir.

Thauban reported:
When the Messenger of Allah (ﷺ) finished his prayer, he would pray forgiveness three times. Walid reported: I said to Auza'i: How Is the seeking of forgiveness? He replied: You should say:

TRANSLATION:
I ask Allah for forgiveness.

It was narrated from Aishah that when the Messenger of Allah (ﷺ) sat in a gathering or prayed, he (ﷺ) said some words, and Aishah asked him about those words. He (ﷺ) said: "If he has spoken some good words (and he says this statement of remembrance), it will be a seal for them to preserve them until the Day of Resurrection, and if he has said something other than that, it (these words) will be an expiation for him:

TRANSLATION:
Glory and praise be to You, O Allah, I seek Your forgiveness and I repent to You.

It was narrated that Al-Bari' said:
When we prayed behind the Messenger of Allah (ﷺ), we liked to be on his right so that his face would turn towards us. And I heard him say:

TRANSLATION:
O Lord, save me from Your punishment on the Day when You resurrect or gather Your slaves.

Thauban reported:
When the Messenger of Allah (ﷺ) finished his prayer, he would pray forgiveness three times and said:

TRANSLATION:
O Allah! You are Peace, and peace comes from You; Blessed are You, O Possessor of Majesty and Honour.

Narrated `Amr bin Maimun Al-Audi:
Sa`d used to teach his sons the following words as a teacher teaches his students the skill of writing and used to say that Allah's Messenger (ﷺ) used to seek Refuge with Allah from them (i.e. the evils) at the end of every prayer. The words are:

TRANSLATION:
O Allah!
1) I seek refuge with You from cowardice, and
2) Seek refuge with You from being brought back to a bad stage of old life and
3) Seek refuge with You from the afflictions of the world, and
4) Seek refuge with You from the punishments in the grave.

'All bin Abi Talib narrated that the Prophet (ﷺ) would say after the Taslim:

TRANSLATION:
O Allah! Forgive me what I have done, and what I have yet to do, and what I have done in private, and what I have done in public, and all my excesses, and all that You know of me. You are the One Who brings forward and distances.

Narrated Warrad:
Once Al-Mughira dictated to me in a letter addressed to Muawiya that the Prophet (ﷺ) used to say after every compulsory prayer,

TRANSLATION:
There is no Deity but Allah, Alone, no Partner to Him. His is the Kingdom and all praise, and Omnipotent is He. O Allah! Nobody can hold back what you gave, nobody can give what You held back, and no struggler's effort can benefit against You.

Hisham narrated that Abu Az-Zubair said:
Ibn Az-Zubair used to say, following every prayer, after he had said the Taslim:

He said: The Messenger of Allah (ﷺ) used to recite these words following every prayer.

TRANSLATION:
There is none worthy of worship but Allah alone, with no partner or associate. His is the Dominion, to Him be praise, and He is Able to do all things. There is no power and no strength except with Allah. There is none worthy of worship but Allah and we worship none but Him. To Him belong all grace and favor, and to Him be glorious praise. There is none worthy of worship but Allah and we are sincere in faith and devotion to Him even though the disbelievers may detest it.

PROPHET MUHAMMAD (ﷺ) said:
Whoever recites Aayat al-Kursi (QURAN 2:255) immediately after each prescribed prayer, there will be nothing standing between him and his entering Paradise except death.

TRANSLATION:
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.

Narrated 'Uqbah bin 'Amir:
The Messenger of Allah (ﷺ) ordered me to recite Al-Mu'awwidhatain (Surah Falaq & Surah Naas) at the end of every Salat.

SURAH FALAQ:
QURAN 113:1 Say, "I seek refuge in the Lord of daybreak
QURAN 113:2 From the evil of that which He created
QURAN 113:3 And from the evil of darkness when it settles
QURAN 113:4 And from the evil of the blowers in knots
QURAN 113:5 And from the evil of an envier when he envies."

SURAH NAAS:
QURAN 114:1 Say, "I seek refuge in the Lord of mankind,
QURAN 114:2 The Sovereign of mankind.
QURAN 114:3 The God of mankind,
QURAN 114:4 From the evil of the retreating whisperer -
QURAN 114:5 Who whispers [evil] into the breasts of mankind -
QURAN 114:6 From among the jinn and mankind."

Narrated Abu Huraira:
The people said, "O Allah's Messenger (ﷺ)! The rich people have got the highest degrees of prestige and the permanent pleasures (in this life and the life to come in the Hereafter)." He said, "How is that?" They said, "The rich pray as we pray, and strive in Allah's Cause as we do, and spend from their surplus wealth in charity, while we have no wealth (to spend likewise)." He said, "Shall I not tell you a thing, by doing which, you will catch up with those who are ahead of you and supersede those who will come after you; and nobody will be able to do such a good deed as you do except the one who does the same (deed as you do). That deed is to recite 'Subhan Allah ten times, and 'Al-Hamdulillah ten times, and 'Allahu Akbar' ten times after every prayer."

It was narrated from Abu Hurairah - and this is the Hadith of Qutaibah - that the poor Muhajirin came to the Messenger of Allah and said: "The people of great wealth have taken the highest ranks and eternal bliss." He said: "Why is that?" They said: "They offer
Salat as we offer Salat and they fast as we fast, but they give in charity and we do not, and they free slaves and we do not." The
Messenger of Allah said: "Shall I not teach you something by means of which you may catch up with those who have gone ahead of you, and go ahead of those who come after you, and there will be no one who is better than you except those who do as you do?" They said: Yes, Messenger of Allah. "He said: "Glorify Allah, extol His greatness, and praise Him at the end of every prayer, thirty-three times." “Suhail said: 'Eleven (times each), eleven (times each), and all of that adds up to thirtythree.’"

Zaid bin Thabit (ra) said:
“We were ordered to say the Tasbīḥ at the end of every Salat thirty-three times, and to say the Takbīr thirty-four times.” He said: “Then a man from the Ansar had a dream in which someone said: ‘The Messenger of Allah (ﷺ) ordered you to say the Tasbīḥ at the end of every Salat thirty-three times, and to say the Taḥmīd thirty-three times, and to say the Takbīr thirty-four times?’ He said: ‘Yes.’ He said: ‘Then make them twenty-five (each) and add the Tahlīl (saying Lā ilāha illallāh) to them.’ The next day he went to the Prophet (ﷺ) and informed him, so he said: “Do it.”

Narrated Abu Hurairah
Some poor people came to the Prophet and said, "The wealthy people will get higher grades and will have permanent enjoyment, and they offer Salat (prayer) like us and observe Saum (fast) as we do. They have more money by which they perform the Hajj, and 'Umra; fight and struggle in Allah's Cause and give in charity." The Prophet said, "Shall I not tell you a thing upon which if you acted you would catch up with those who have surpassed you? Nobody would overtake you and you would be better than the people amongst whom you live except those who would do the same. Say Subhan Allah, Alhamdu-lillah and Allahu Akbar thirty-three times each after every (compulsory) Salat (prayer) ." We differed and some of us said that we should say Subhãn Allah thirty three times and Alhamdu lillãh thirty-three times and Allahu Akbar thirty-four times. I went to the Prophet who said, "Say, Subhan Allah and Alhamdulillah and Allahu Akbar all of them for thirty three times."

Remembrance after (the prayer), the one who says them or does them after each obligatory prayer will not be disappointed: Thirty-three Tasbihah, thirty-three Tahmiah and thirty-four Takbirah.

Zaid bin Thabit (ra) said:
“We were ordered to say the Tasbīḥ at the end of every Salat thirty-three times, and to say the Takbīr thirty-four times.” He said: “Then a man from the Ansar had a dream in which someone said: ‘The Messenger of Allah (ﷺ) ordered you to say the Tasbīḥ at the end of every Salat thirty-three times, and to say the Taḥmīd thirty-three times, and to say the Takbīr thirty-four times?’ He said: ‘Yes.’ He said: ‘Then make them twenty-five (each) and add the Tahlīl (saying Lā ilāha illallāh) to them.’ The next day he went to the Prophet (ﷺ) and informed him, so he said: “Do it.”