The Melitzer Rebbe shlit'a taught me the secrets of praying with a niggun (melody), as follows:
1. A niggun speaks the heart's deepest emotions, and is far more expressive than words.
2. A niggun rises higher and faster than words.
3. Prayer in words only is subject to a bombardment of outside thoughts and disturbances that destroy kavonna, or intent. A niggun focuses prayer by uniting the brain and the heart. The stronger and better-focused the prayer, the more resistant it is to the Yetzer Hora (evil inclination), who tries to destroy the prayer or block its ascent.
4. A niggun helps a person cling to Hashem almost instantly; when one clings to Hashem, nothing can block prayer.
5. A niggun cleanses the soul, and facilitates the wonderful emotional releases of tears and laughter.
The Melitzer Rebbe shlit'a also quoted an advice from the Ariza'l for anything that ails or troubles a person: During Shacharis (morning prayers), if one should sing Shiras HaYam word for word and in the niggun of Torah reading.
***Here's a Lazer secret: When I really need to use heavy spiritual artillery, like pleading to Hashem to give someone the blessing of children or to save someone from a terminal disease, I use Guy Tzvi Mintz's niggun, "Dibbur Shel Teshuva" - the tears flow...
Have a wonderful week, with smiles and blessings!