Easton's Bible Dictionary:

Prayer is converse with God; the intercourse of the soul with God, not in contemplation or meditation, but in direct address to him. Prayer may be oral or mental, occasional or constant, ejaculatory or formal. It is a "beseeching the Lord" (Ex. 32:11); "pouring out the soul before the Lord" (1 Sam. 1:15); "praying and crying to heaven" (2 Chr. 32:20); "seeking unto God and making supplication" (Job 8:5); "drawing near to God" (Ps. 73:28); "bowing the knees" (Eph. 3:14).

Prayer presupposes a belief in the personality of God, his ability and willingness to hold intercourse with us, his personal control of all things and of all his creatures and all their actions.

Acceptable prayer must be sincere (Heb. 10:22), offered with reverence and godly fear, with a humble sense of our own insignificance as creatures and of our own unworthiness as sinners, with earnest importunity, and with unhesitating submission to the divine will. Prayer must also be offered in the faith that God is, and is the hearer and answerer of prayer, and that he will fulfil his word, "Ask, and ye shall receive" (Matt. 7:7, 8; 21:22; Mark 11:24; John 14:13, 14), and in the name of Christ (16:23, 24; 15:16; Eph. 2:18; 5:20; Col. 3:17; 1 Pet. 2:5).

Prayer is of different kinds, secret (Matt. 6:6); social, as family prayers, and in social worship; and public, in the service of the sanctuary.

Intercessory prayer is enjoined (Num. 6:23; Job 42:8; Isa. 62:6; Ps. 122:6; 1 Tim. 2:1; James 5:14), and there are many instances on record of answers having been given to such prayers, e.g., of Abraham (Gen. 17:18, 20; 18:23-32; 20:7, 17, 18), of Moses for Pharaoh (Ex. 8:12, 13, 30, 31; Ex. 9:33), for the Israelites (Ex. 17:11, 13; 32:11-14, 31-34; Num. 21:7, 8; Deut. 9:18, 19, 25), for Miriam (Num. 12:13), for Aaron (Deut. 9:20), of Samuel (1 Sam. 7:5-12), of Solomon (1 Kings 8; 2 Chr. 6), Elijah (1 Kings 17:20-23), Elisha (2 Kings 4:33-36), Isaiah (2 Kings 19), Jeremiah (42:2-10), Peter (Acts 9:40), the church (12:5-12), Paul (28:8).

No rules are anywhere in Scripture laid down for the manner of prayer or the attitude to be assumed by the suppliant. There is mention made of kneeling in prayer (1 Kings 8:54; 2 Chr. 6:13; Ps. 95:6; Isa. 45:23; Luke 22:41; Acts 7:60; 9:40; Eph. 3:14, etc.); of bowing and falling prostrate (Gen. 24:26, 52; Ex. 4:31; 12:27; Matt. 26:39; Mark 14:35, etc.); of spreading out the hands (1 Kings 8:22, 38, 54; Ps. 28:2; 63:4; 88:9; 1 Tim. 2:8, etc.); and of standing (1 Sam. 1:26; 1 Kings 8:14, 55; 2 Chr. 20:9; Mark 11:25; Luke 18:11, 13).

If we except the "Lord's Prayer" (Matt. 6:9-13), which is, however, rather a model or pattern of prayer than a set prayer to be offered up, we have no special form of prayer for general use given us in Scripture.

Prayer is frequently enjoined in Scripture (Ex. 22:23, 27; 1 Kings 3:5; 2 Chr. 7:14; Ps. 37:4; Isa. 55:6; Joel 2:32; Ezek. 36:37, etc.), and we have very many testimonies that it has been answered (Ps. 3:4; 4:1; 6:8; 18:6; 28:6; 30:2; 34:4; 118:5; James 5:16-18, etc.).

"Abraham's servant prayed to God, and God directed him to the person who should be wife to his master's son and heir (Gen. 24:10-20).

"Jacob prayed to God, and God inclined the heart of his irritated brother, so that they met in peace and friendship (Gen. 32:24-30; 33:1-4).

"Samson prayed to God, and God showed him a well where he quenched his burning thirst, and so lived to judge Israel (Judg. 15:18-20).

"David prayed, and God defeated the counsel of Ahithophel (2 Sam. 15:31; 16:20-23; 17:14-23).

"Daniel prayed, and God enabled him both to tell Nebuchadnezzar his dream and to give the interpretation of it (Dan. 2: 16-23).

"Nehemiah prayed, and God inclined the heart of the king of Persia to grant him leave of absence to visit and rebuild Jerusalem (Neh. 1:11; 2:1-6).

"Esther and Mordecai prayed, and God defeated the purpose of Haman, and saved the Jews from destruction (Esther 4:15-17; 6:7, 8).

"The believers in Jerusalem prayed, and God opened the prison doors and set Peter at liberty, when Herod had resolved upon his death (Acts 12:1-12).

"Paul prayed that the thorn in the flesh might be removed, and his prayer brought a large increase of spiritual strength, while the thorn perhaps remained (2 Cor. 12:7-10).

"Prayer is like the dove that Noah sent forth, which blessed him not only when it returned with an olive-leaf in its mouth, but when it never returned at all.", Robinson's Job.

(taken from Easton's Bible Dictionary prepared for God's Word for Windows version 2.0)

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Genesis 4:26 And to Seth, to him also there was born a son; and he called his name Enos: then began men to call upon the name of the LORD.

Genesis 32:24 And Jacob was left alone; and there wrestled a man with him until the breaking of the day.

25 And when he saw that he prevailed not against him, he touched the hollow of his thigh; and the hollow of Jacob's thigh was out of joint, as he wrestled with him.

26 And he said, Let me go, for the day breaketh. And he said, I will not let thee go, except thou bless me.

27 And he said unto him, What is thy name? And he said, Jacob.

28 And he said, Thy name shall be called no more Jacob, but Israel: for as a prince hast thou power with God and with men, and hast prevailed.

29 And Jacob asked him, and said, Tell me, I pray thee, thy name. And he said, Wherefore is it that thou dost ask after my name? And he blessed him there.

30 And Jacob called the name of the place Peniel: for I have seen God face to face, and my life is preserved.

Luke 18:1 And he spake a parable unto them to this end, that men ought always to pray, and not to faint;

Mark 9:29 And he said unto them, This kind can come forth by nothing, but by prayer and fasting.

Matthew 6:6 But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.

7 But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking.

8 Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him.

9 After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.

10 Thy kingdom come. Thy will be done in earth, as it is in heaven.

11 Give us this day our daily bread.

12 And forgive us our debts, as we forgive our debtors.

13 And lead us not into temptation, but deliver us from evil: For thine is the kingdom, and the power, and the glory, for ever. Amen.

Isaiah 55:6 Seek ye the LORD while he may be found, call ye upon him while he is near:

7 Let the wicked forsake his way, and the unrighteous man his thoughts: and let him return unto the LORD, and he will have mercy upon him; and to our God, for he will abundantly pardon.

Psalms 145:18 The LORD is nigh unto all them that call upon him, to all that call upon him in truth.

19 He will fulfil the desire of them that fear him: he also will hear their cry, and will save them.

20 The LORD preserveth all them that love him: but all the wicked will he destroy.

2 Chronicles 7:14 If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin, and will heal their land.

1 Chronicles 16:11 Seek the LORD and his strength, seek his face continually.

Genesis 32:24 And Jacob was left alone; and there wrestled a man with him until the breaking of the day.

25 And when he saw that he prevailed not against him, he touched the hollow of his thigh; and the hollow of Jacob's thigh was out of joint, as he wrestled with him.

26 And he said, Let me go, for the day breaketh. And he said, I will not let thee go, except thou bless me.

27 And he said unto him, What is thy name? And he said, Jacob.

28 And he said, Thy name shall be called no more Jacob, but Israel: for as a prince hast thou power with God and with men, and hast prevailed.

29 And Jacob asked him, and said, Tell me, I pray thee, thy name. And he said, Wherefore is it that thou dost ask after my name? And he blessed him there.

30 And Jacob called the name of the place Peniel: for I have seen God face to face, and my life is preserved.

1 Corinthians 14:15 What is it then? I will pray with the spirit, and I will pray with the understanding also: I will sing with the spirit, and I will sing with the understanding also.

Ephesians 6:18 Praying always with all prayer and supplication in the Spirit, and watching thereunto with all perseverance and supplication for all saints;

Philippians 4:6 Be careful for nothing; but in every thing by prayer and supplication with thanksgiving let your requests be made known unto God.

1 Thessalonians 5:17 Pray without ceasing.

1 Timothy 2:8 I will therefore that men pray every where, lifting up holy hands, without wrath and doubting.

Hebrews 4:16 Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need.

Jude 1:20 But ye, beloved, building up yourselves on your most holy faith, praying in the Holy Ghost,

Revelation 5:8 And when he had taken the book, the four beasts and four and twenty elders fell down before the Lamb, having every one of them harps, and golden vials full of odours, which are the prayers of saints.

Revelation 8:3 And another angel came and stood at the altar, having a golden censer; and there was given unto him much incense, that he should offer it with the prayers of all saints upon the golden altar which was before the throne.

Revelation 8:4 And the smoke of the incense, which came with the prayers of the saints, ascended up before God out of the angel's hand.

Proverbs 1:23 Turn you at my reproof: behold, I will pour out my spirit unto you, I will make known my words unto you.

24 Because I have called, and ye refused; I have stretched out my hand, and no man regarded;

25 But ye have set at nought all my counsel, and would none of my reproof:

26 I also will laugh at your calamity; I will mock when your fear cometh;

27 When your fear cometh as desolation, and your destruction cometh as a whirlwind; when distress and anguish cometh upon you.

28 Then shall they call upon me, but I will not answer; they shall seek me early, but they shall not find me:

29 For that they hated knowledge, and did not choose the fear of the LORD:

30 They would none of my counsel: they despised all my reproof.

31 Therefore shall they eat of the fruit of their own way, and be filled with their own devices.

Notice that it is possible after the ark of Noah was closed the people outside were crying out to Noah to let them in...it was too late...

Public Prayers of Christ, Mat. 11:25; Luke 3:21; John 11:47; 17:1.

Requests of for Prayer, I Sam. 7:8; 12:19; I Kings 13:6; Acts 8:24; ....more

Unwise Prayers, Num. 11:15; I Kings 19:4; Jona 4:3; Matt. 20:21.

Prayers for Food, Gen. 28:20; Prov. 30:8; Matt. 6:11.

Prayers for the Church John 17:20; Rom. 1:9; Eph. 1:16; 3:14; Philemon. 1:4; Col. 1:3; 4:12; 1 Th. 1:2.

Exodus 2:23 And it came to pass in process of time, that the king of Egypt died: and the children of Israel sighed by reason of the bondage, and they cried, and their cry came up unto God by reason of the bondage.

Exodus 14:10 And when Pharaoh drew nigh, the children of Israel lifted up their eyes, and, behold, the Egyptians marched after them; and they were sore afraid: and the children of Israel cried out unto the LORD.

Exodus 17:4 And Moses cried unto the LORD, saying, What shall I do unto this people? they be almost ready to stone me.

Jud. 3:9; 4:3; 6:7; 1 Sam. 7:9; 1 Kings 17:20; 1 Chr. 5:20; 2 Chr. 13:14; 14:11; Ps. 34:6; 61:2; Lam. 2:18.