All About Eve might be the ultimate classic drama. It doesn't do anything to play with the genre or attempt to twist it in any way. It features masterful performances, a traditional character arc, and features the bad guy, Eve, getting punished in the end.
Even though Eve isn't a psychological thriller, we can see roots of it in similar modern-day psychological thrillers. You know the ones, where the girl (or guy) introduced at the beginning of the movie turns out to be not so innocent, and really has it in for the protagonist. The main characters in these movies, like Bridget Fonda in Single White Female (1992) or Cristal Connors in Showgirls(1997) or the famous writer in Misery (1990), never see the crazy train coming. However, because of All About Eve, we know to be suspicious of anyone who says they're your #1 fan.
As Cristal says, "There's always someone younger and hungrier coming down the stairs after you" (source).