Here are each of the 5 staffs Gandalf wields in the Lord of the Rings movies, and when he acquires each of them. Ian McKellen's wizard is undoubtedly one of the most magnetic figures in Peter Jackson's Middle-earth movies, with prominent roles in both The Hobbit and The Lord of the Rings trilogies. Ever the enigma, Gandalf is a free spirit who works in mysterious ways, but never fails to aid his friends or fight on the side of good. Gandalf's chief arc in Tolkien's story is his fall as Gandalf the Grey and his glorious rebirth as Gandalf the White, but this transformation isn't the only time he switches magic wand.
Throughout The Lord of the Rings, the Fellowship are blessed with new weapons, upgrades and items that represent their allies, their history, or their personal progression. For example, Frodo is gifted with the Phial of Galadriel, which signifies his friendship with the elves, while the reforging of Narsil marks Aragorn taking his rightful throne in Return of the King. Gandalf also reaps the benefit of some inventory improvements, especially with regards to his staff, and even though he only has 2 variations in the books (one as "the Grey" and one as "the White") there are many more on-screen.
The Opening Flower
This is chronologically the first staff Gandalf is seen using in Peter Jackson's films, and makes its debut in The Hobbit: An Unexpected Journey. Nicknamed the "Opening Flower" after the design of its tip, the staff was crafted by the Elves and is presumably the first instrument the wizard wields after being sent to Middle-earth. However, this staff is withered away into dust when Gandalf engages the growing presence of Sauron in The Desolation of Smaug.
Radagast's Spare
Following his original staff's destruction, Gandalf borrows a spare from his old wizarding pal, Sylvester McCoy's Radagast the Brown. This iteration is seen in the titular conflict of the final movie in the Hobbit trilogy, The Battle of Five Armies but, presumably because it was borrowed from another, it isn't as effective as Gandalf's original staff.
Radagast's Staff Dwindled
The staff Gandalf inherits from Radagast is damaged over time, which causes the branches on the tip to wear down and the wood to discolor. Nevertheless, Gandalf sticks by his weapon of choice and carries this broken replacement into The Fellowship of the Ring, and is the first staff viewers see Ian McKellen's character holding in real-time. When Saruman defeats Gandalf and imprisons him atop the Tower of Orthanc, he obviously relieves the wizard of his staff, and Gandalf escapes without it.
The Rivendell Staff
Fortunately, it isn't long before Gandalf is given another replacement when he and the Hobbits are reunited at Rivendell. Elrond's hospitality ensures the newly-formed Fellowship depart well-stocked, and this includes a new staff for the group's resident magician. This staff seems to be an improvement upon its predecessor, but it both debuts and departs in The Fellowship of the Ring, with Gandalf losing the item after falling to the Balrog in the Mines of Maria. In the books, Gandalf's Lord of the Rings staff breaks during this battle, but he merely loses it in the movies.
The White Staff
The most obvious staff change in The Lord of the Rings comes when Gandalf returns as Gandalf the White in The Two Towers. After losing to the Balrog, Gandalf is appointed as Saruman's replacement after the latter's betrayal, and receives a heavenly upgrade in terms of his clothes, his magical power and, of course, his staff. The white rod itself was actually a gift from Galadriel, but it too is destroyed in Return of the King by the Witch-King of Angmar. As Gandalf, Frodo and the Elves prepare to depart the Grey Havens, the white staff has been restored, and appears bigger than before, but whether repaired of replaced, the design is identical, rather a completely new staff in its own right.