'All Manner of Prayer'

"Pray...with [all manner of] prayer..." (Eph.6:18AMP).

Some manner of prayer I can think of in the New Testament: 

1. The prayer of yielding to God's will ("Not my will, but thine be done")

2. Intercession

3. Supplication

4. Petition

5. Desiring

6. Asking

7. Saying/Speaking/Commanding ("...whosoever shall say to this mountain, be thou removed and be thou cast into the sea...he shall have whatsoever he saith...")

8. Agreeing together in prayer

9. Praise and Worship

10. Thanksgiving

11. Praying with the understanding

12. Praying with the spirit

13. Praying to oneself and to God with an unknown tongue

14. Groanings of the Spirit

15. Praying in the Spirit

16. Praying together with others

17. Prayer of handing over ("casting your cares upon Him")

18. The prayer of faith ("believe ye receive them, and ye shall have them"; "and shall not doubt in his heart, but shall believe that those things which he saith shall come to pass"; "and all things, whatsoever ye shall ask in prayer, believing, ye shall receive")

19. Calling upon the Lord - e.g., for salvation.

And more...