Allah Almighty says in the Qur'an:
"When my servants ask you concerning me, (tell them) I am indeed close (to them). I listen to the prayer of every suppliant when he calls on me." [2:186] The place of duaa is so high to Allah, that the Prophet had said: "Nothing is more honourable to Allah the Most High than du`a."
[Sahih al-Jami` no.5268].
He also said: "The most excellent worship is du`a."
[Sahih Al-Jami` no. 1133];
and in order to warn those who are arogant, or careless in making duaa, the Prophet said: "The most incapable person is the one who does not make du`a, and the most miserly person is the one who does not give salaam."
[Sahih Al-Jami` no. 1055],
and further, said: "If one does not ask Allah, He will get angry with him."
[Sahih al-Jami` no.2414]
Allah is the Glorious and the Mighty, the answerer of every person in need and every person with a request. Indeed Allah is free of all wants, and He is answerable to non. We have no other god, but Him, whilst He has many servants other than us. Indeed Allah has revealed:
"O mankind! It is you who stand in need of Allah, but Allah is Rich (Free of all wants and needs), Worthy of All Praise."
So to fulfill our needs and wants, we must call on Him. Making Du'a to Allah, is a recognition of our weakness and His greatness. The Prophet had said: "Ask Allah for everything, even the lace of your shoes. If Allah does not provide, it will never be available."
[Ibn al-Sunni, no. 349 - hasan. Supported by at-Tirmidhi 4/298 and others.]
And let not there be anyone who says: "... my Lord won't answer my prayer, because of this and that.. or because of so and so..". No! Indeed Allah is the Most Generous King. Is there anyone who met a king, and praised and glorified him, and then asked, yet the request was not granted? So what about Allah, the King of the Heavens and the Earth - who has total control over your life, your wealth and your future. Why would He not grant you your request? Indeed, our beloved Prophet had said: "Verily your Lord is the One modest and Generous, and when His servant raises his hands to Him in supplication, He is diffident (in some wordings, shy or hesitant) from returning them empty."
[Ahmad, Abu Dawud and at-Tirmidhi - Hasan]
[Hadith checking from Sheikh Hussain al-'Awayishah's "Kitab ad-Dua". An english translation has been published by JIMAS.]