WASHINGTON—The retirement of Anthony M. Kennedy brings to an end the tenure of one of the Supreme Court’s most consequential modern-day justices, the author of landmark rulings on gay rights, the death penalty and campaign finance and one of the last bearers of the case-by-case jurisprudence and old-fashioned politesse that once marked the court.

In his typically low-key manner, Justice Kennedy held his plans close Wednesday, surprising even fellow justices when he announced his retirement at their private gathering following...