Allah said:

﴿وَاسْتَغْفِرُواْ اللَّهَ إِنَّ اللَّهَ غَفُورٌ رَّحِيمٌ﴾

(...and ask Allah for His forgiveness. Truly, Allah is Oft-Forgiving, Most-Merciful.)

Allah frequently orders remembrance of Him after acts of worship are finished. Muslim reported that Allah's Messenger used to ask Allah for His forgiveness thrice after the prayer is finished. It is reported in the Two Sahihs that the Prophet encouraged Tasbih (saying Subhan Allah, i.e., Glorified is Allah), Tahmid (saying Al-Hamdu Lillah, i.e., praise be to Allah) and Takbir (saying Allahu Akbar, i.e., Allah is the Most Great) thirty-three times each (after prayer).

Ibn Marduwyah collected the Hadith that Al-Bukhari reported from Shaddad bin Aws, who stated that Allah's Messenger said:

«سَيِّدُ الْاِسْتِغْفَارِ أَنْ يَقُولَ الْعَبْدُ: اللَّهُمَّ أَنْتَ رَبِّي، لَا إِلهَ إِلَّا أَنْتَ، خَلَقْتَنِي وَأَنَا عَبْدُكَ، وَأَنَا عَلى عَهْدِكَ وَوَعْدِكَ مَا اسْتَطَعْتُ، أَعُوذُ بِكَ مِنْ شَرِّ مَا صَنَعْتُ، أَبُوءُ لَكَ بِنِعْمَتِكَ عَلَيَّ، وَأَبُوءُ بِذَنْبِي، فَاغْفِرْ لِي فَإِنَّهُ لَا يَغْفِرُ الذُّنُوبَ إلَّا أَنْتَ، مَنْ قَالَهَا فِي لَيْلَةٍ فَمَاتَ فِي لَيْلَتِهِ دَخَلَ الْجَنَّــةَ، وَمَنْ قَالَهَا فِي يَوْمِهِ فَمَاتَ دَخَلَ الْجَنَّــة»

(The master of supplication for forgiveness, is for the servant to say: `O Allah! You are my Lord, there is no deity worthy of worship except You. You have created me and I am Your servant. I am on Your covenant, as much as I can be, and awaiting Your promise. I seek refuge with You from the evil that I have committed. I admit Your favor on me and admit my faults. So forgive me, for none except You forgives the sins.' Whoever said these words at night and died that same night will enter Paradise. Whoever said it during the day and died will enter Paradise.)

Furthermore, it is reported in the Two Sahihs that `Abdullah bin `Amr said that Abu Bakr said, "O Messenger of Allah! Teach me an invocation so that I may invoke (Allah) with it in my prayer. He told me to say:

«قُلْ: اللَّهُمَّ إِنِّي ظَلَمْتُ نَفْسِي ظُلْمًا كَثِيرًا وَلَا يَغْفِرُ الذُّنُوبَ إِلَّا أَنْتَ فَاغْفِرْ لِي مَغْفِرَةً مِنْ عِنْدِكَ، وَارْحَمْنِي إِنَّكَ أَنْتَ الْغَفُورُ الرَّحِيم»

(Allahumma inni zalamtu nafsi zulman kathiran, wa la yaghfirudh-dhunuba illa Anta faghfirli maghfiratan min `indika, war-hamni innaka Antal-Ghafur-ur-Rahim (O Allah! I have done great injustice to myself and none except You forgives sins, so please forgive me and be merciful to me as You are the Forgiver, the Merciful).)

There are many other Hadiths on this subject.

﴿فَإِذَا قَضَيْتُم مَّنَـسِكَكُمْ فَاذْكُرُواْ اللَّهَ كَذِكْرِكُمْ ءَابَآءَكُمْ أَوْ أَشَدَّ ذِكْرًا فَمِنَ النَّاسِ مَن يَقُولُ رَبَّنَآ ءَاتِنَا فِى الدُّنْيَا وَمَا لَهُ فِى الاٌّخِرَةِ مِنْ خَلَـقٍ - وِمِنْهُم مَّن يَقُولُ رَبَّنَآ ءَاتِنَا فِى الدُّنْيَا حَسَنَةً وَفِي الاٌّخِرَةِ حَسَنَةً وَقِنَا عَذَابَ النَّارِ - أُولَـئِكَ لَهُمْ نَصِيبٌ مِّمَّا كَسَبُواْ وَاللَّهُ سَرِيعُ الْحِسَابِ ﴾

(200. So when you have accomplished your Manasik, remember Allah as you remember your forefathers or with far more remembrance. But of mankind there are some who say: "Our Lord! Give us (Your bounties) in this world!'' and for such there will be no portion in the Hereafter.) (201. And of them there are some who say: "Our Lord! Give us in this world that which is good and in the Hereafter that which is good, and save us from the torment of the Fire!'') (202. For them there will be alloted a share for what they have earned. And Allah is swift at reckoning.)