God commands prayer of His people (Luke 18:1; Ephesians 6:18; Colossians 4:2; I Thessalonians 5:17), and provides His Son and Spirit for intercession (Romans 8:26, 34; Heb 7:25).
Some things for which we should pray (not intended to be exhaustive):
Pray for those that persecute you (Matt. 5:44; Luke 6:28).
Pray for God's Kingdom come and His will be done in earth (Matt. 6:10).
Pray for God to provide your daily needs (Matt. 6:11).
Pray for God's forgiveness (Matt. 6:12).
Pray for deliverance from evil (Matt. 6:13).
Pray for children (Matt. 19:13).
Pray that fall not into temptation (Luke 22:40; Matt. 6:13).
Pray for boldness to proclaim the word of God (Acts 4:29; Eph. 6:18-20).
Pray for the salvation of Israel (Romans 10:1).
Pray for filling with the knowledge of God's will (Col. 1:9).
Pray for open doors to speak the gospel (Col. 4:3; 2 Thess. 3:1).
Pray for other Christians (1 Thess. 5:25; Heb 13:18) .
Pray for authorities, and all men generally (1 Tim. 2:1-2).
Pray for wisdom (James 1:5).
Pray for healing (James 5:13,16).