Types of biblical prayers:

Confession (Psalm 51; Luke 18:10-24)
Praise (1 Chronicles 29:10-13; Luke 1:46-55)
Thanksgiving (Psalm 105:1-7; 1 Thessalonians 5:16-18)
Petition (Genesis 24:12-14; Acts 1:24-26)
Intercession (Exodus 32:11-13; Philippians 1:9-11)
Commitment (1 Kings 8:56-61; Acts 4:24-30)
Forgiveness (Daniel 9:4-19; Acts 7:60)
Confidence (Psalm 23; Luke 2:29-32)
Benediction (Numbers 6:24-26; Jude 24)