The drawn-out execution of an Arizona man is certain to set off more public debate over the death penalty and lead to new court battles over states' efforts to keep details about their lethal-injection practices secret.

The execution of Joseph R. Wood III on Wednesday in Florence, Ariz., took nearly two hours and was marked by lengthy, repeated bouts of labored breathing on the part of Mr. Wood, according to various accounts of the execution. The 55-year-old was convicted of shooting to death his estranged girlfriend and her...