The Grand Nagus' staff, also called the Sceptre of the Grand Nagus, was an item that was held by the Ferengi Grand Nagus. (DS9: "The Nagus", "Rules of Acquisition", "The Search, Part I") It was traditional for an individual to kiss the head of the staff upon receiving advice from the Nagus. (DS9: "The Nagus", "The Search, Part I")
The Grand Proxy could carry a replica of the staff as a symbol of the authority granted to him by the Grand Nagus. (VOY: "False Profits")
In 2371, Zek gave the staff to Benjamin Sisko to prove to Quark that he wanted him to help the USS Defiant to locate the Founders. (DS9: "The Search, Part I")
While living in the Vic's Las Vegas Lounge holoprogram, Nog commented that a cane given to him by Vic Fontaine (a replica of a cane used by Errol Flynn) was reminiscent of the Grand Nagus' staff. (DS9: "It's Only a Paper Moon")
As he passed the reigns of power to Rom, Zek also gave him the staff, a symbol of the power it represented. (DS9: "The Dogs of War")
The Grand Nagus' staff was sold off in the It's A Wrap! sale and auction, though the bottom half was broken off and missing. 
In Star Trek Online, Nog carries the staff with him to get another Ferengi to surrender a Krenim artifact. He later reveals that it wasn't the actual staff but Rom's "second best".