Benefits of Duaa

Abu Hurairah  narrates from Rasool-Allah , "Do duaa to Allah with this confidence that HE will accept it and know this well that Allah doesn't accept the duaa done with a negligent and careless heart. (Tirmizi)
Salman Farsi  narrates from Rasool-Allah , "Duaa turns away destiny and good deeds lengthen age. (Tirmizi)
Umar  narrates that, "Whenever Rasool-Allah  raised his hands for duaa He  did not put down them down until HE  took both hands over his face." (Tirmizi)
Aisha (Radi Allahu Anha) narrates that, "Rasool-Allah  liked duaas that were inclusive and he left the rest." (Abu Dawood)
Abdullah bin Umar  narrates from Rasool-Allah , "Duaa for a person not present is accepted quickly by Allah." (Tirmizi and Abu Dawood)

Abu Hurairah  narrates from Rasool-Allah , "Three duaas are such in which there is no doubt of their acceptance: 1) Father's duaa 2) Traveler's duaa 3) Duaa of the oppressed". (Timizi, Ibne Majah)
Abu Hurairah  narrates from Rasool-Allah , "Three types of people's duaas are not rejected: 1) At the time of iftar the person who has fasted 2) Adil ruler's duaa 3) The duaa of the oppressed. Allah raises the duaa of the oppressed on the clouds and the doors of heaven are opened for it and Allah says, "Oath of MY Majesty and Honour! I will help and aid you. Even though if the help is after few days." (Tirmizi)