The Mevlevi order
The Mevlevi Order has for seven centuries offered spiritual training based on the principles of Sufism. It is a rigorous path of initiation and service continually adapting itself to changing circumstances and times. The Mevlevi Order traces back to Mevlâna Jalâluddîn Rumi (d. 1273) one of the greatest mystics and poets the world has ever known. Historically it has been Rumi, more than any other Sufi, who has issued the invitation to people of all backgrounds to the mystical garden that is Sufism:
For more than seven centuries the Mevlevi Order has held the light of the religion of love, offering spiritual refuge and enlightenment for those who wished to develop their human-ness to the highest level. In Ottoman times the Mevlevi Order cultivated not only spiritual attainment but cultural and artistic excellence as well. Mevlevis have always been progressive and liberal in spirit while at the same time conserving the best of tradition. Today, the Mevlevi Order is reviving in the West.
The Naqshbandi Sufi Order has, in recent years, incorporated the practice of whirling as a meditation and devotion.
For more on the Mevlevi Order and Whirling Dervishes, see: http://en.wikipedia.org/wiki/Mevlevi