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A Treasury of Prayers
Our Father (The Lord's Prayer)
Our Father who art in heaven, hallowed be Thy name, Thy kingdom come, Thy will be done
on earth as it is in heaven.  Give us this day our daily bread; and forgive us our trespasses
as we forgive those who trespass against us; and lead us not into temptation, but deliver us from evil.  For Thine is the Kingdom and the power and the glory forever and ever.  Amen
The Jesus Prayer   (which may be used repeatedly and at any time and in any place)
Lord Jesus Christ, Son of God, have mercy on me, a sinner. 
Daily Intercessions
Intercession of a Spouse
for One's Marriage
Prayer of Preparation
before Holy Communion
Prayer for the Departed (The Dead)
Intercession of Parents for their Children
(or Pastors for their Parishioners)
The Catechism Evening Prayers
The Catechism Morning Prayers
Morning Prayer
LEX ORANDI - Some Classic Prayers of the Christian Church:

While prayers we formulate on our own are by all means to be encouraged, there is also in Christendom a rich store-house of  prayers that Christians from many generations and many places have found to be of enormous help in their own prayer-life.
Prayer of St. Francis
Lord, make me an instrument of Your peace.  Where there is hatred, let me sow love; where there is injury, pardon; where there is discord, union; where there is doubt, faith; where there is despair, hope; where there is darkness, light; where there is sadness, joy.  Grant that I may not so much seek to be consoled, as to console; to be understood, as to understand; to be loved, as to love.  For it is in giving that we receive and it is in pardoning that we are pardoned and it is in dying that we are born to eternal life.
Prayer of St. Ignatius Loyola
Teach me, good Lord, to serve You as You deserve; to give and not to count the cost, to fight and not to heed the wounds; to toil and not to seek to rest; to labor and not to ask for any reward, save that of knowing I do Your will, through Jesus Christ, our Lord. 
Prayer of St. Ephraem, the Syrian
O Lord and Master of my life, do not give me the spirit of sloth, despair, lust of power, and idle talk. But give rather a spirit of chastity, humility, patience, and love to Your servant.  Yes, Lord and King, grant me to see my own transgressions and not to judge my brother, for blessed are You unto ages of ages.      
St Patrick's Breastplate
Christ be with me, Christ within me, Christ behind me, Christ before me, Christ beside me, Christ to win me, Christ to comfort and restore me; Christ in quiet, Christ in danger, Christ in hearts of all that love me, Christ in mouth of friend and stranger.  I bind unto myself the name, the strong name of the Trinity, by invocation of the same, the Three-in-One and One-in-Three, of whom all nature has creation: Eternal father, Word and Spirit; Praise to the God of my salvation, salvation is of Christ the Lord. 
On Prayer
Have Mercy on Me
A New Year's Prayer
The Jesus Prayer