^As I said, I don't know exactly how much of the Istari's powers are dependant of the staff, as this isn't specified in the texts to my knowledge.
All I'm saying is that they do seem of utmost importance, probably with both a symbolic and a practical significance.
When Sauruman's staff is broken his powers seem vastly decreased as someone already mentioned. He's still a slick talker and well able to cause trouble on a small scale, but no longer a threat to Middle Earth.
And when Gandalf does his fire tricks, the staff is always involved, I believe.
Whether Gandalf could have cured Theoden without his magic tricks, only Eru knows (well perhaps Manwe as well
)