In 1991, the Spanish newspaper El País published an article centered on a dispute between Madrid plastic surgeon Hugo Guidotti Russo and one of his patients over an allegedly botched breast surgery. The headline: "The Risk of Wanting to Be Slim."

Nearly 20 years later, Dr. Guidotti Russo, backed by Spain's privacy regulator, contends that the tale of the dispute is personal information and wants to purge the article from Google, where it shows up on the first page of results when his name is searched.

His...