Gregory House usually walks with a cane in House M.D.
House uses the cane because of permanent leg damage caused by an infarction in his quadriceps muscle. The injury leaves him with chronic pain and a limp, which become defining physical features of the character.
The cane is not merely a prop. House sometimes uses it to support himself, point during conversations, or create distance from other people. His dependence on pain medication is also a continuing part of the series’ story, although the show presents addiction and medical treatment dramatically rather than as a clinical guide.
Some viewers remember House’s limp more strongly than the specific object, but his characteristic mobility aid is a cane. He does not generally use a walker, and a crutch is not his regular instrument.