Bowser steals the Star Rod from Star Haven at the beginning of Paper Mario and uses it to grant all of his wishes. Mario must save the 7 Star Spirits to deactivate the power of the Star Rod.
It was later seen in Super Smash Brothers Melee, as an attack item.
The Star Rod is also Boo and Dry Bones' special orb in Mario Party 7. It makes the user invisible and doubles their Dice Block roll for 2 turns.
The Star Rod is most likely taken from the Kirby series.