Ps. 65:2; Acts 10:34, 35: "O Hearer of prayer, even to you people of all flesh will come." "God is not partial, but in every nation the man that fears him and works righteousness is acceptable to him."
Luke 11:2: "Whenever you pray, say, `Father, let your name be sanctified.'"
John 14:6, 14: "Jesus said to him: `I am the way and the truth and the life. No one comes to the Father except through me. If you ask anything in my name, I will do it.'"
1 John 5:14: "This is the confidence that we have toward him, that, no matter what it is that we ask according to his will, he hears us." (To have such confidence, however, you must first know God's will. Then be sure that your requests are in harmony with it.)
1 Pet. 3:12: "The eyes of Jehovah are upon the righteous ones, and his ears are toward their supplication; but the face of Jehovah is against those doing bad things."
1 John 3:22: "Whatever we ask we receive from him, because we are observing his commandments and are doing the things that are pleasing in his eyes."
Isa. 55:6, 7: "Search for Jehovah, you people, while he may be found. Call to him while he proves to be near. Let the wicked man leave his way, and the harmful man his thoughts; and let him return to Jehovah, who will have mercy upon him, and to our God, for he will forgive in a large way." (Mercifully, Jehovah invites even persons who have done bad things to call to him in prayer. But, to have God's approval, they must sincerely repent of their wrong ways and thoughts and change their course.)
For more, see:
Drawing Close to God in Prayer - In 16 well-illustrated lessons, this brochure presents the Bible's basic teachings.
Draw Close to God in Prayer - How does God answer our prayers?
Does Praying Do Any Good?
God Does Answer Prayers
Why Should You Pray?
How Should We Pray to God?
Teach Us How to Pray
You Must Pray This Way
How Can I Improve in My Prayers?
The Power of Prayer
The Lord's Prayer - Its Meaning for You