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."

http://www.alquranic.com/articles/mail244.html