House's apartment number in House M.D. is 221B.
The address is a direct reference to 221B Baker Street, the fictional London residence of Sherlock Holmes. House is deliberately modeled in part on Holmes: both are exceptionally perceptive investigators, both solve apparently impossible cases through deduction, and both can be difficult companions because of their arrogance and unconventional methods.
The connection goes beyond the apartment number. House's surname echoes Holmes's, his friend Wilson parallels Dr. Watson, and the medical mysteries function like detective stories. House often begins with a seemingly impossible puzzle, generates competing explanations, and tests each hypothesis until the evidence supports one diagnosis.
The address is not meant to imply that House lives in London. The series places him in New Jersey, and the Baker Street reference is an Easter egg for viewers familiar with Arthur Conan Doyle's detective. 221A, 221C, and 221D are plausible-looking variations, but 221B is the canonical Holmes address and the number used for House's apartment in the series.