One way to answer this question is to look at what the early church prayed for. Here is a list gathered from the New Testament. It can guide you in how you pray. I suggest that periodically you pray through this list just to test whether your prayers are leaving out anything the New Testament included. We don't have to pray all of these each time we pray. But over time it would be good if our prayers had the breadth and depth of the New Testament prayers.
They called on God to exalt his name in the world.
Pray then like this: Our Father who art in heaven, Hallowed be thy name (Matthew 6:9).
They called on God to extend his kingdom in the world.
Thy kingdom come. Thy will be done, On earth as it is in heaven (Matthew 6:10 ).
They called on God that the gospel would run and triumph.
Finally, brethren, pray for us, that the word of the Lord may speed on and triumph, as it did among you (2 Thessalonians 3:1).
They called on God for the fullness of the Holy Spirit.
If you then, who are evil, know how to give good gifts to your children, how much more will the heavenly Father give the Holy Spirit to those who ask him! (Luke 11:13; cf. Ephesians 3:19).
They called on God to vindicate his people in their cause.
And will not God vindicate his elect, who cry to him day and night? Will he delay long over them? (Luke 18:7).
They called on God to save unbelievers.
Brethren, my heart's desire and prayer to God for them is that they may be saved (Romans 10:1).
They called on God to direct the use of the sword.
"Take the sword of the Spirit, which is the word of God, praying through all prayer and supplication on every occasion . . ." (Ephesians 6:17-18)
They called on God for boldness in proclamation.
Pray at all times in the Spirit . . . and also for me, that utterance may be given me in opening my mouth boldly to proclaim the mystery of the gospel (Ephesians 6:18-19)
And now, Lord, look upon their threats, and grant to thy servants to speak thy word with all boldness (Acts 4:29).
They called on God for signs and wonders.
And now Lord . . . grant your servants to speak thy word with boldness . . . while you stretch out your hand to heal, and signs and wonders are performed through the name of thy holy servant Jesus (Acts 4:30).
Elijah was a man of like nature with ourselves and he prayed fervently that it might not rain, and for three years and six months it did not rain on the earth. Then he prayed again and the heaven gave rain, and the earth brought forth its fruit (James 5:17 -18).
They called on God for the healing of wounded comrades.
Let them pray over him, anointing him with oil in the name of the Lord, and the prayer of faith will save the sick man and the Lord will raise him up (James 5:14-15).
They called on God for the healing of unbelievers.
It happened that the father of Publius lay sick with fever and dysentery; and Paul visited him and prayed, and putting his hands on him healed him (Acts 28:8).
They called on God for the casting out of demons.
And he said to them, "This kind cannot be driven out by anything but prayer" (Mark 9:29)
They called on God for miraculous deliverances.
So Peter was kept in prison; but earnest prayer for him was made to God by the church . . . When he realized [he had been freed], he went to the house of Mary, the mother of John whose other name was Mark, where many were gathered together and were praying (Acts 12:5,12).
But about midnight Paul and Silas were praying and singing hymns to God, and the prisoners were listening to them, and suddenly there was a great earthquake (Acts 16:25-26).
They called on God for the raising of the dead.
But Peter put them all outside and knelt down and prayed; then turning to the body he said, "Tabitha, rise." And she opened her eyes, and when she saw Peter she sat up (Acts 9:40).
They called on God to supply his troops with necessities.
Give us this day our daily bread (Matthew 6:11).
They called on God for strategic wisdom.
If any of you lacks wisdom, let him ask God, who gives to all men generously and without reproaching, and it will be given him (James 1:5).
They called on God to establish leadership in the outposts.
And when they had appointed elders for them in every church, with prayer and fasting they committed them to the Lord in whom they believed (Acts 14:23).
They called on God to send out reinforcements.
Pray therefore the Lord of the harvest to send out laborers into his harvest (Matthew 9:38).
While they were worshiping the Lord and fasting, the Holy Spirit said, "Set apart for me Barnabas and Saul for the work to which I have called them." Then after fasting and praying they laid their hands on them and sent them off (Acts 13:2-3).
They called on God for the success of other missionaries.
I appeal to you, brethren, by our Lord Jesus Christ and by the love of the Spirit, to strive together with me in your prayers to God on my behalf, that I may be delivered from the unbelievers in Judea, and that my service for Jerusalem may be acceptable to the saints, (Romans 15:30-31).
They called on God for unity and harmony in the ranks.
I do not pray for these only, but also for those who believe in me through their word, that they may all be one; even as thou, Father, art in me, and I in thee, that they also may be in us, so that the world may believe that thou hast sent me (John 17:20-21).
They called on God for the encouragement of togetherness.
[We are] praying earnestly night and day that we may see you face to face and supply what is lacking in your faith? (1 Thessalonians 3:10).
They called on God for a mind of discernment.
And it is my prayer that your love may abound more and more in with knowledge and all discernment, so that you may approve what is excellent, and may be pure and blameless for the day of Christ (Philippians 1:9-10).
They called on God for a knowledge of his will.
And so, from the day we heard of it, we have not ceased to pray for you, asking that you may be filled with the knowledge of his will in all spiritual wisdom and understanding (Colossians 1:9).
They called on God to know him better.
[We have not ceased to pray for you to be] increasing in the knowledge of God (Colossians 1:10 ; cf. Ephesians 1:17 ).
They called on God for power to comprehend the love of Christ.
I bow my knees before the Father . . . that you may have power to comprehend with all the saints what is the breadth and length and height and depth and to know the love of Christ which surpasses knowledge (Ephesians 3:14,18).
They called on God for a deeper sense of assured hope.
I do not cease to give thanks for you, remembering you in my prayers . . . that you may know what is the hope to which he has called you, what are the riches of his glorious inheritance in the saints (Ephesians 1:16,18).
They called on God for strength and endurance.
[We have not ceased to pray for you to be] strengthened with all power, according to his glorious might, for all endurance and patience with joy (Colossians 1:11 ; cf. Ephesians 3:16).
They called on God for deeper sense of his power within them.
I do not cease to give thanks for you, remembering you in my prayers . . . that you may know . . . what is the immeasurable greatness of his power toward us who believe (Ephesians 1:16, 19).
They called on God that their faith not be destroyed.
I have prayed for you that your faith may not fail; and when you have turned again, strengthen your brethren (Luke 22:32).
Watch at all times, praying that you may have strength to escape all these things that will take place, and to stand before the Son of man (Luke 21:36).
They called on God for greater faith.
Immediately the father of the child cried out and said, "I believe; help my unbelief!" (Mark 9:24 ; cf. Ephesians 3:17).
They called on God that they might not fall into temptation.
Lead us not into temptation (Matthew 6:13).
Watch and pray that you may not enter into temptation; the spirit indeed is willing, but the flesh is weak (Matthew 26:41).
They called on God that he would complete their resolves.
To this end we always pray for you, that our God may make you worthy of his call, and may fulfil every good resolve and work of faith by his power (2 Thessalonians 1:11).
They called on God that they would do good works.
[We have not ceased to pray for you that you] lead a life worthy of the Lord, fully pleasing to him, bearing fruit in every good work (Colossians 1:10).
They called on God or forgiveness for their sins.
Forgive us our debts as we forgive our debtors (Matthew 6:12).
They called on God for protection from the evil one.
Deliver us from evil (Matthew 6:13).
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