For the Christian, the answer is both yes and no. Yes, we should fear God because He is the Almighty Creator who can discipline us should we rebel against Him. He is so holy and so awesome that being in His presence brings an inspiring fear. Consider Isa. 6:4-5 where Isaiah has a vision of God's majesty and glory: "and the foundations of the thresholds trembled at the voice of him who called out, while the temple was filling with smoke. 5 Then I said, Woe is me, for I am ruined! Because I am a man of unclean lips, and I live among a people of unclean lips." Isaiah isn't the only one who had such an encounter. Gideon thought he would die when he saw the angel of the Lord face to face (Judges 6:22). Manoah also thought he would die after encountering God (Judges 13:22). When anyone experiences the Majesty of the Lord, he naturally is humbled and the awesome greatness of God automatically produces a normal and healthy fear.
On the other hand, we do not need to fear God regarding judgment. As Christians, we have escaped the righteous judgment of God in the person of Jesus (Romans 8:1). We have nothing to fear on the Day of Judgment because Christ took our place and bore the judgment of God on our behalf. “He who believes in Him is not judged; he who does not believe has been judged already, because he has not believed in the name of the only begotten Son of God," (John 3:18).