It is such a worthwhile exercise to get all of Paul's actual prayers, put them side-by-side and read and reflect on them all together in one go. Here's a list i've put together. What we can learn from this for our pray is mind boggling. All of these prayers I think are for Christians, except for this first one. Even that says a lot!
1Brothers, my heart's desire and prayer to God for the Israelites is that they may be saved.
5May the God who gives endurance and encouragement give you a spirit of unity among yourselves as you follow Christ Jesus, 6so that with one heart and mouth you may glorify the God and Father of our Lord Jesus Christ.
13May the God of hope fill you with all joy and peace as you trust in him, so that you may overflow with hope by the power of the Holy Spirit.
2 Corinthians 13
7Now we pray to God that you will not do anything wrong. Not that people will see that we have stood the test but that you will do what is right even though we may seem to have failed. 8For we cannot do anything against the truth, but only for the truth. 9We are glad whenever we are weak but you are strong; and our prayer is for your perfection.
15For this reason, ever since I heard about your faith in the Lord Jesus and your love for all the saints, 16I have not stopped giving thanks for you, remembering you in my prayers. 17I keep asking that the God of our Lord Jesus Christ, the glorious Father, may give you the Spirit of wisdom and revelation, so that you may know him better. 18I pray also that the eyes of your heart may be enlightened in order that you may know the hope to which he has called you, the riches of his glorious inheritance in the saints, 19and his incomparably great power for us who believe. That power is like the working of his mighty strength, 20which he exerted in Christ when he raised him from the dead and seated him at his right hand in the heavenly realms, 21far above all rule and authority, power and dominion, and every title that can be given, not only in the present age but also in the one to come. 22And God placed all things under his feet and appointed him to be head over everything for the church, 23which is his body, the fullness of him who fills everything in every way.
14For this reason I kneel before the Father, 15from whom his whole family in heaven and on earth derives its name. 16I pray that out of his glorious riches he may strengthen you with power through his Spirit in your inner being, 17so that Christ may dwell in your hearts through faith. And I pray that you, being rooted and established in love, 18may have power, together with all the saints, to grasp how wide and long and high and deep is the love of Christ, 19and to know this love that surpasses knowledge--that you may be filled to the measure of all the fullness of God. 20Now to him who is able to do immeasurably more than all we ask or imagine, according to his power that is at work within us, 21to him be glory in the church and in Christ Jesus throughout all generations, for ever and ever! Amen.
9And this is my prayer: that your love may abound more and more in knowledge and depth of insight, 10so that you may be able to discern what is best and may be pure and blameless until the day of Christ, 11filled with the fruit of righteousness that comes through Jesus Christ--to the glory and praise of God.
9For this reason, since the day we heard about you, we have not stopped praying for you and asking God to fill you with the knowledge of his will through all spiritual wisdom and understanding. 10And we pray this in order that you may live a life worthy of the Lord and may please him in every way: bearing fruit in every good work, growing in the knowledge of God, 11being strengthened with all power according to his glorious might so that you may have great endurance and patience, and joyfully 12giving thanks to the Father, who has qualified you to share in the inheritance of the saints in the kingdom of light. 13For he has rescued us from the dominion of darkness and brought us into the kingdom of the Son he loves, 14in whom we have redemption, the forgiveness of sins.
1 Thessalonians 3
9How can we thank God enough for you in return for all the joy we have in the presence of our God because of you? 10Night and day we pray most earnestly that we may see you again and supply what is lacking in your faith. 11Now may our God and Father himself and our Lord Jesus clear the way for us to come to you. 12May the Lord make your love increase and overflow for each other and for everyone else, just as ours does for you. 13May he strengthen your hearts so that you will be blameless and holy in the presence of our God and Father when our Lord Jesus comes with all his holy ones.
1 Thessalonians 5
23May God himself, the God of peace, sanctify you through and through. May your whole spirit, soul and body be kept blameless at the coming of our Lord Jesus Christ. 24The one who calls you is faithful and he will do it.
2 Thessalonians 1
11With this in mind, we constantly pray for you, that our God may count you worthy of his calling, and that by his power he may fulfill every good purpose of yours and every act prompted by your faith. 12We pray this so that the name of our Lord Jesus may be glorified in you, and you in him, according to the grace of our God and the Lord Jesus Christ.
2 Thessalonians 2
16May our Lord Jesus Christ himself and God our Father, who loved us and by his grace gave us eternal encouragement and good hope, 17encourage your hearts and strengthen you in every good deed and word.
2 Thessalonians 3
2And pray that we may be delivered from wicked and evil men, for not everyone has faith. 3But the Lord is faithful, and he will strengthen and protect you from the evil one. 4We have confidence in the Lord that you are doing and will continue to do the things we command. 5May the Lord direct your hearts into God's love and Christ's perseverance.
2 Thessalonians 3
16Now may the Lord of peace himself give you peace at all times and in every way. The Lord be with all of you.