Gregory House is famously addicted to Vicodin in House M.D.
Vicodin is a prescription painkiller containing hydrocodone and paracetamol, also known as acetaminophen. In the series, House uses it to manage chronic pain caused by an infarction that damaged muscles in his right thigh. His dependence on the medication becomes a continuing medical, professional, and personal conflict.
The drug is not simply a character accessory. House's use affects his judgment, relationships, employment, and treatment decisions, and several storylines address attempts to stop or control his dependence. The show also portrays withdrawal and relapse as major parts of his character arc.
Other prescription medicines appear in the series, but Vicodin is the specific drug most closely associated with House. It should not be confused with OxyContin, Percocet, or Adderall, which have different formulations or uses and are not the canonical answer to this question.