Allah Accepts and Answers Dua

[40.Surah Momin : Ayah 60]

And your Lord says: Call upon Me, I will answer you."

[2.Surah Al-Baqarah : Ayah 186]

"And when My servants ask you concerning Me, then surely I am very near; I answer the prayer of the suppliant when he calls on Me, so they should answer My call and believe in Me that they may walk in the right way."
[27.Surah Naml : Ayah 62]

"Or, Who answers the distressed one when he calls upon Him and removes the evil, and He will make you successors in the earth. Is there a god with Allah? Little is it that you mind!"
[7.Surah Al-Ar'af]

Ayah 55:
"Call on your Lord humbly and secretly; surely He does not love those who exceed the limits."
Ayah 56:
"And call on Him fearing and hoping; surely the mercy of Allah is nigh to those who do good (to others)."
Ayah 205:
"And remember your Lord within yourself humbly and fearing and in a voice not loud in the morning and the evening and be not of the heedless ones."
Duas of Some Prophets

[21.Surah Al-Anbiyaa]
Seven Persons on Allah's Shade
[Sahih Bukhari: Volume 1, Book 11, Number 629]
Narrated Abu Huraira (Radi Allah Anhu): The Prophet (sal-allahu-alleihi-wasallam) said, "Allah will give shade, to seven, on the Day when there will be no shade but His. These seven persons are
1) a just ruler,
2) a youth who has been brought up in the worship of Allah (i.e. worships Allah sincerely from childhood),
3) a man whose heart is attached to the mosques (i.e. to pray the compulsory prayers in the mosque in congregation),
4) two persons who love each other only for Allah's sake and they meet and part in Allah's cause only,
5) a man who refuses the call of a charming woman of noble birth for illicit intercourse with her and says: I am afraid of Allah,
6) a man who gives charitable gifts so secretly that his left hand does not know what his right hand has given (i.e. nobody knows how much he has given in charity),
7) and a person who remembers Allah in seclusion and his eyes are then flooded with tears."