He loses his original staff (by breaking it) in his fight with the Balrog.
At that moment Gandalf lifted his staff, and crying aloud he smote the bridge before him. The staff broke asunder and fell from his hand. A blinding sheet of white flame sprang up. The bridge cracked. Right at the Balrog's feet it broke, and the stone upon which it stood crashed into the gulf, while the rest remained, poised, quivering like a tongue of rock thrust out into emptiness.
The Lord of the Rings: The Fellowship of the Ring, Book II, Chapter V, The Bridge of Khazad-Dum
That's it, really. He gets a new one after he's resurrected and doesn't lose that one. The movies feature many of his staffs breaking, but in the books, it happens only one time.
So Peter Jackson didn't invent Gandalf's staff breaking.
Gandalf's new staff after the fight with the Balrog in the books:
Well met, I say again!' said the old man, coming towards them. When he was a few feet away, he stood, stooping over his staff, with his head thrust forward, peering at them from under his hood.
The Lord of the Rings: The Two Towers, Book III, Chapter V, The White Rider