God promises to answer our prayers in 1 John 5:14,15 (ESV):
And this is the confidence we have towards Him, that if we ask anything according to His will He hears us. And if we know that He hears us in whatever we ask, we know that we have the requests that we have asked of Him.Prayer is an awesome gift from an awesome God.
The toughest part of prayer (to me) is grasping how and when prayer is answered. At times our prayers are answered almost instantly, completely, and recognizably; often nothing seems to happen at all. Since God always answers prayers, and when I'm unable to detect a positive answer, I can only assume He has denied my petition, or at least delayed it until a more opportune time.
Praying with selfish intent or for things harmful to us as Christians, and not receiving what we ask for is understandable, but millions of Christians praying for the lives of the starving and dying Jews during the Holocaust doesn't seem like a selfish endeavor, yet over six million men, women, and children were murdered during the Third Reich in spite of countless prayers on their behalf. Perhaps my miniscule brain doesn't have enough horsepower to fully comprehend the workings and thoughts of God..... Yep, that's it!
It all boils down to faith; by faith I believe that God, being perfect, accomplishes exactly what He desires. It's not within me to understand everything God sets in motion in His creation, but after reflecting on His perfection and total love for us, we have no alternative but to recognize His unerring decisions and live according to His will, which often means our prayers will be answered negatively for our own good, the good of others, or how it fits into His overall plan for His people.