All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If you mean the acts which the Prophet supplicated to Allaah to have mercy upon its doer and the like, then such acts are so many and it is not possible to mention them all in one Fatwa, but we will mention some of them.
1- Shaving the head or trimming it for the pilgrim and it is better for a male pilgrim to shave his head. ‘Abdullaah Ibn ‘Umar narrated that the Prophet said: “O Allaah have mercy upon those who shave their heads.” The Companions asked: “What about those who only trim their heads?” He said: “O Allaah have mercy upon those who shave their heads.” They again asked: “What about those who only trim their heads?” He said: “And those who trim their heads.” [Al-Bukhari and Muslim]
2- A spouse waking up his/her partner for the night prayer: The Prophet said: “May Allaah have mercy upon a husband who wakes up by night and prays and wakes up his wife, and if she refuses to wake up, he splashes water on her face, and may Allaah have mercy upon a wife who wakes up by night and prays and wakes up her husband, and if he refuses to wake up, she splashes water on his face.” [Abu Daawood and Ibn Maajah]
3- Seeking people's forgiveness for the rights one owes them: The Prophet said: “May Allaah have mercy upon a person who has wronged his (Muslim) brother with regard to his honor or money, and he came to him and sought his forgiveness before it [his right] will be taken from him on a day [the Day of Judgment] where there is no longer any Dinaar nor Dirham; and if he has any good deeds, they will be taken from him [to recompense for the person whom he wronged], and if he has no good deeds, some of the bad deeds of his counterpart will be added to his burden.” [At-Tirmithi]
This is all what we can mention at the moment and if you look for more acts in this regard, you may find many.
Allaah Knows best.