Read the Necessity and Power of Prayer by St. Alphonsus Ligouri, Doctor of the Church.
Read the Treatise on Prayer and Meditation by St. Peter of Alcantara.
The absolutely best prayer is the Holy Sacrifice of the Mass. Check the Liturgy section for details. The next best prayer is the Holy Rosary (see also Apostolic Letter On the Most Holy Rosary Rosarium Virginis Mariae).
Pope John Paul II asked us to say the St. Michael prayer "to obtain help in the battle against forces of darkness."
Read about the power of one Hail Mary.
For a good collection of prayers, we recommend the Baltimore Prayer Book, Secret of the Rosary, Favorite Catholic Prayers and Novenas, and Manual of Practical Devotion to St. Joseph.
See also the Enchiridion of Indulgences for more prayers that have indulgences attached. Indulgenced prayers are indicated by a in the list below.