LONDON—Antony Sher, one of the most acclaimed Shakespearean actors of his generation, has died aged 72, the Royal Shakespeare Company said Friday. Sher had been diagnosed with terminal cancer earlier this year. His husband, Royal Shakespeare Company Artistic Director Gregory Doran, took leave from his job to care for him. Born in Cape Town, South Africa, in 1949, Sher moved to Britain in the late 1960s to study drama. He joined the RSC in 1982 and had a breakthrough role in 1984 as the usurping king in “Richard III.” He went on to play most of Shakespeare’s meaty male roles, including Falstaff in the “Henry IV” plays, Leontes in “The Winter’s Tale,” Shylock in “The Merchant of Venice,” Iago in “Othello” and the title characters in “Macbeth” and “King Lear.” Non-Shakespearean roles for the company, based in the Bard’s hometown of Stratford-upon-Avon, included Willy Loman in Arthur Miller’s “Death of …