All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad 
  is His slave and Messenger.
There are numerous sound narrations stating that the Prophet 
  in many situations used to carry a stick (staff) in his hand. 'Aa'ishah 
  narrated that the Prophet 
  was waiting for Jibreel (Gabriel), 
  but he did not come in time. The Prophet 
  was holding a stick in his hand and he threw it away. [Al-Bukhari]
The various Hadeeth in this context are not construed to imply that the Prophet 
  used to carry the stick to give the impression that it is a ritual practice or it has religious implication, so as to be considered a Sunnah (Prophetic tradition). It is understood by scholars to be a worldly habit.
The jurist Ibn al-Arabi 
  in his book 'Ahkam al-Qur'an' stated that, "Some people are trying hard to show the numerous benefits of carrying a stick as if they were doing so to interpret what Moosa (Moses) 
  said about his stick or rod:  'and in it I find other uses.' This is an unnecessary effort and each incident should be taken according to its merits. It is agreed upon by the majority of scholars that carrying the stick is Sunnah in one situation, namely, during sermons. The other use of the stick for which there is no consensus is the use of the stick for leaning on it during voluntary prayer. It is narrated that the Prophet 
  authorized the use of the stick for leaning on it during Nafil prayer. [Abu Daawood and others]
Allaah Knows best.