The Bible is packed with don't be afraid messages. Most of them are encouragements. Some should be warnings.
"The king said to her, 'Do not be afraid; but what do you see?' And the woman said to Saul, 'I see a divine being coming up out of the earth.'" 1 Samuel 28:13 (NAS)
The woman should have been afraid. She was a medium, which was against King Saul's law (even though he was the one hiring her) and against God's law. And really, why would you seek information from any other spirit when you have access to the Holy Spirit? If He doesn't inform you, then you're not supposed to know.
"David said to him, ''Do not fear, for I will surely show kindness to you for the sake of your father Jonathan, and will restore to you all the land of your grandfather Saul; and you shall eat at my table regularly.'" 2 Samuel 9:7 (NAS)
King David took in his late best friend's son, who incidentally would have been an heir to King Saul's throne. Any other king would have killed him to eliminate possible competition, but David had faith in God's anointing on his own life, and was gracious and merciful instead.
"Then Elijah said to her, 'Do not fear; go, do as you have said, but make me a little bread cake from it first and bring it out to me, and afterward you may make one for yourself and for your son.'" 1 Kings 17:13 (NAS)
This lady was out of options and resigned to giving up on life itself, but Elijah, being a man of God, was asking her to have faith. She was rewarded with miraculous provision.
"The angel of the Lord said to Elijah, 'Go down with him; do not be afraid of him.' So he arose and went down with him to the king." 2 Kings 1:15 (NAS)
Elijah had just sent a "you're going to die" message to the king, so naturally he wasn't excited about going to see the king in person when he was sent for. Elijah had ordered fire from the sky to destroy the first two captains with their fifty men apiece who were sent to take him to the king. The third captain came on his knees begging for his and his fifty men's lives, and God told Elijah to go ahead with them. He did, he re-delivered a "you're going to die" message to the king, and the king died. Once again, when you're on a mission for God, He'll see you through it.
"So he answered, 'Do not fear, for those who are with us are more than those who are with them.'" 2 Kings 6:16 (NAS)
Elisha's attendant saw that they were under siege, but Elisha prayed that the attendant would be given the ability to see what was happening in the spiritual realm. The man saw the mountain full of horses and chariots of fire, and the tables were supernaturally turned.
Keep your eyes on the Lord, not the circumstances.