are some examples:   

  • Pray for the people of your nation (Num 21:7)   
  • Pray for your city (Jer 29:7)   
  • Pray for peace in Jerusalem (Ps 122:6)   
  • Pray for your persecutors (Mat 5:43-44; Luke 6:28)   
  • Pray for children (Mat 19:13)
  • Pray for escape from judgment (Luke 21:36) 
  • Pray you will not fall into temptation (Luke 22:40)
  • Pray for Christians (Job 17:9; 1 Thes 5:25; Heb 13:18)
  • Pray for boldness in proclaiming the gospel and for God to do miracles in people's lives (Acts 4:29-31)
  • Pray all the time, be alert, pray for the saints (Eph 6:18)   
  • Pray for fearless preaching (Eph 6:20) 
  • Pray to be filled with the knowledge of His will (Col 1:9)   
  • Pray for open doors for the gospel (Col 4:3) 
  • Pray that the Word of God may be glorified (2 Thes 3:1)
  • Pray for deliverance from evil men (2 Thes 3:2)   
  • Pray for everyone, kings, authorities, peace, quiet, godliness, holiness (1 Tim 2:1,2)
  • Pray for life for dead sinners (1 John 5:16)   

There are other things we are taught to pray for in Scripture, but the point is that we need to follow the Scriptural model of prayer. 

There are only two places where the words "prayer" and "power" are mentioned.
"With 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 fulfil every good purpose of yours and every act prompted by your faith." (2 Thes 1:11)   

He was not praying for them to get power but that God "by His power" would fulfil "every good purpose" of theirs and "every act prompted by your faith". This is by the sovereign will of God, which if followed will produce good works. If God's will is not followed, it can only produce fleshly or demonic fruit. The second reference is this:
"I pray that out of his glorious riches he may strengthen you with power through his Spirit in your inner being, so that Christ may dwell in your hearts through faith. And I pray that you, being rooted and established in love, may have power, together with all the saints, to grasp how wide and long and high and deep is the love of Christ, and to know this love that surpasses knowledge--that you may be filled to the measure of all the fulness of God." (Eph 3:16-19)   

Here again Paul is praying for the Ephesians, not for himself. He prays that