Duas to Recite during and after Salat

Thauban (RA) reported: Whenever the Messenger of Allah (SAW) concluded his prayer, he would beg forgiveness from Allah thrice and then would recite: "Allahumma Antas-Salamu, wa minkas-salamu, tabarakta ya Dhal-Jalali wal-Ikram (O Allah, You are the Grantor of security, and security comes from You. You are Blessing, O You Who have majesty and nobility)!" (Imam) Al-Awza'i, one of the narrators of this Hadith, was asked: "How forgiveness is to be sought?" He answered: "The Messenger of Allah (PBUH) used to say: 'Astaghfirullah! Astaghfirullah! (I beseech Allah for forgiveness, I beseech Allah for forgiveness)'." [Muslim]

Sa'd bin Abu Waqqas (RA) reported: The Messenger of Allah (SAW) used to seek (Allah's) protection after prayers in these words: "Alla-humma inni a'udhu bika minal-jubni wal-bukhl, wa a'udhu bika min an uradda ila ardhalil-'umur, wa a'udhu bika min fitnatid-dunya, wa a'udhu bika min fitnatil-qabr (O Allah, I seek refuge with You from cowardice, miserliness and from being sent back to a feeble age; and, seek refuge with You from the trials of this life and those of the grave)."

Mu'adh (RA) reported: The Messenger of Allah (SAW) took hold of my hand and said, "O Mu'adh! By Allah I love you, so I advise you to never forget to recite after every prayer: "Allahumma a'inni ala dhikrika, wa shukrika, wa husni 'ibadatika (O Allah, help me remember You, to be grateful to You, and to worship You in an excellent manner)."

Abu Hurairah (RA) reported: The Messenger of Allah (SAW) said, "When anyone of you has done his Tashahhud during Salat (prayer), he should seek refuge in Allah against four things and say: "Allahumma inni a'udhu bika min 'adhabi jahannam, wa min 'adhabil-qabr, wa min fitnatil-mahya wal-mamat, wa min sharri fitnatil-masihid-dajjal (O Allah! I seek refuge in you from the torment of Hell, from the torment of the grave, from the trials of life and death, and from the mischief of Al-Masih Ad-Dajjal (Antichrist)."

'Ali (RA) reported: When the Messenger of Allah (SAW) was in Salat (prayer), he used to supplicate towards the end of prayer after Tashahhud and before the concluding salutations: "Allahum-maghfir li ma qaddamtu wa ma akh-khartu, wa ma asrartu, wa ma a'lantu, wa ma asraftu, wa ma Anta a'lamu bihi minni. Antal-Muqqadimu, wa Antal-Mu'akh-khiru. La ilaha illa Anta (O Allah! Forgive my former and latter sins, which I have done secretly and those which I have done openly, and that I have wronged others, and those defaults of mine about which you have better knowledge than I have. You alone can send whomever you will to Jannah, and You Alone can send whomever you will to Hell-fire. None has the right to be worshipped but you."