One may say that the best du'a for forgiveness is the one preserved in the immutable text of the Qur'an 7:23 in the following words:

 قَالَا رَبَّنَا ظَلَمْنَا أَنفُسَنَا وَإِن لَّمْ تَغْفِرْ لَنَا وَتَرْحَمْنَا لَنَكُونَنَّ مِنَ الْخَاسِرِينَ 

They said, "Our Lord, we have wronged ourselves, and if You do not forgive us and have mercy upon us, we will surely be among the losers."

There are also many other supplications (ad'iya) available to any Muslim seeking forgiveness from Allah (swt) for one's sins and shortcomings. Many beautiful and eloquent expressions have been taught by the Prophet Muhammad (s) and his family the Ahl al-Bayt (a).

For instance, check out this Du'a of Repentance taught by Imam 'Ali Zayn al-'Abidin (a) who was the son of Imam al-Husayn b. 'Ali (a) and the fourth Imam.