A New Jersey mafia boss under strain who finds himself in a psychiatrist’s office. A 30-something writer taking on the big city with her friends. A “Mother of Dragons” locked in an epic battle to sit on an iron throne.

During Richard Plepler’s almost three decades at HBO, the premium cable channel has shaped culture with unforgettable characters and groundbreaking shows that have forced viewers to grapple with topics like power, politics and sex. Often, the magic of such television series is the messy way those themes intersect.

Mr. Plepler joined HBO as a public relations official in 1992 and rose through the ranks. He abruptly stepped down as C.E.O. on Thursday. Here is a look at some of the network’s biggest hits during his tenure at the company.