But instead of watching comedies like “The Hangover” or “Broad City,” Americans are watching dramas like “Contagion” on Netflix NFLX, +0.84%,renting “Donnie Darko” on Amazon Prime, YouTube GOOG, +0.50% GOOGL, +0.63% and iTunes AAPL, +0.61% and “The Handmaid’s Tale” on Hulu DIS, +2.90%.