In Scripture, in many different passages and to various people we find angels or prophets (or even the Lord Himself) bearing messages - and so often the first words heard are "fear not." When an angel carried a message to God's people, he usually was reminding them of God's promises, of their prayers which were about to be fulfilled, or some unexpected danger that the Lord would protect them from.
1) Fear not - though there are spiritual battles, the Lord will answer your prayers:
Daniel 10:12 Then said he unto me, Fear not, Daniel: for from the first day that thou didst set thine heart to understand, and to chasten thyself before thy God, thy words were heard, and I am come for thy words.
2) Fear not, if you repent of your sins and turn back to me, I will have mercy upon you:
1 Samuel 12:19-20 And all the people said unto Samuel, Pray for thy servants unto the LORD thy God, that we die not: for we have added unto all our sins this evil, to ask us a king. And Samuel said unto the people, Fear not: ye have done all this wickedness: yet turn not aside from following the LORD, but serve the LORD with all your heart;
Job 11:14-18 If iniquity be in thine hand, put it far away, and let not wickedness dwell in thy tabernacles. For then shalt thou lift up thy face without spot; yea, thou shalt be stedfast, and shalt not fear: Because thou shalt forget thy misery, and remember it as waters that pass away: And thine age shall be clearer than the noonday; thou shalt shine forth, thou shalt be as the morning. And thou shalt be secure, because there is hope; yea, thou shalt dig about thee, and thou shalt take thy rest in safety.
3) Fear not those false prophets that I have not sent:
Deuteronomy 18:22 When a prophet speaketh in the name of the LORD, if the thing follow not, nor come to pass, that is the thing which the LORD hath not spoken, but the prophet hath spoken it presumptuously: thou shalt not be afraid of him.
4) Fear not, for I am your peace and will give you peace:
Judges 6:23-24 And the LORD said unto him, Peace be unto thee; fear not: thou shalt not die. Then Gideon built an altar there unto the LORD, and called it Jehovahshalom: unto this day it is yet in Ophrah of the Abiezrites.
John 14:27 Peace I leave with you, my peace I give unto you: not as the world giveth, give I unto you. Let not your heart be troubled, neither let it be afraid.
5) Fear not death or sudden fear:
Psalms 56:3 What time I am afraid, I will trust in thee.
Psalms 91:4-6 He shall cover thee with his feathers, and under his wings shalt thou trust: his truth shall be thy shield and buckler. Thou shalt not be afraid for the terror by night; nor for the arrow that flieth by day; Nor for the pestilence that walketh in darkness; nor for the destruction that wasteth at noonday. (See also verses 1-2)
Psalms 112:7 He shall not be afraid of evil tidings: his heart is fixed, trusting in the LORD.
Song of Solomon 3:8 They all hold swords, being expert in war: every man hath his sword upon his thigh because of fear in the night. (In this allegory, I believe we can apply this to one aspect of spiritual warfare: using the sword of the Spirit - the Word of God - to resist the fear that Satan may at times attempt to alarm us by.)
Isaiah 12:2 Behold, God is my salvation; I will trust, and not be afraid: for the LORD JEHOVAH is my strength and my song; he also is become my salvation.
Romans 8:15 For ye have not received the spirit of bondage again to fear; but ye have received the Spirit of adoption, whereby we cry, Abba, Father.
Hebrews 2:14-15 Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil; And deliver them who through fear of death were all their lifetime subject to bondage.
6) Fear not when you apply your heart unto wisdom from God's Word:
Proverbs 1:33 But whoso hearkeneth unto me shall dwell safely, and shall be quiet from fear of evil.
Proverbs 3:23-26 Then shalt thou walk in thy way safely, and thy foot shall not stumble. When thou liest down, thou shalt not be afraid: yea, thou shalt lie down, and thy sleep shall be sweet. Be not afraid of sudden fear, neither of the desolation of the wicked, when it cometh. For the LORD shall be thy confidence, and shall keep thy foot from being taken.