In a sea of late-90s rom-com takes on classic literature, “10 Things I Hate About You” stood out for remaining faithful to its Shakespearean roots. Based on “The Taming of the Shrew,” the film centered on the Stratford girls, whose strict father won’t allow Bianca (Larisa Oleynik) to date until her older sister, Kat (Julia Stiles), does. The problem: Kat has no use for boys; she’s got her sights set on college. Hoping to go out with Bianca, new student Cameron James (Joseph Gordon-Levitt) hatches a convoluted plan to get Patrick Verona (Heath Ledger) to date the prickly Kat. Of course, drama, romance and a lot of awkward moments ensue.

What stands out 20 years later is the movie’s continued relevance — its Seattle teenagers debate sexual politics — as well as its status as a beloved teen comedy. Made for $11.2 million, “10 Things I Hate About You” was released on March 31, 1999, and made instant stars out of Stiles, Gordon-Levitt and Ledger.

But things could have turned out differently because several actors you know could have ended up as the leads.

I recently spoke with the stars (including Gabrielle Union and David Krumholtz), the director Gil Junger and others about casting near-misses, face-drawing and their memories of Ledger, who died of an accidental prescription-drug overdose in 2008. Here are edited excerpts from the conversations.