House commonly uses a cane because of his leg injury in House M.D.
The cane is one of Dr. Gregory House's most recognizable visual traits. He walks with a pronounced limp after permanent muscle damage to his right thigh, and the cane helps him move while also reinforcing the character's distinctive silhouette.
House's cane is not merely a prop. He uses it in comedic business, points with it, and occasionally changes its appearance. The show also connects his chronic pain and dependence on medication to his medical history and behavior.
A cane is different from a crutch: a crutch generally transfers more body weight away from a leg, while House's single cane supports his walking pattern. His leg condition itself is a separate fact from the device he uses.