There's a lot that goes into making a great villain. One of those things is their relationship with the hero. Often, villains are a heck of a lot more interesting when they have a real history with their opponent - or at least an interesting dynamic. The same applies to the heroes: sometimes, it's more fun to see them locked in conflict that's a little more personal than a standard clash between good versus evil.
What are the most interesting hero-villain relationships in anime? There are plenty to choose from. One classic example is Vash the Stampede and Knives Millions from Trigun, twin brothers with wildly different views on humanity. More recently in The Promised Neverland, there's the relationship between Isabella, the supposedly loving caretaker of Gracefield House, and the orphans fighting desperately to escape her.
Which dynamics keep you interested? Vote them up!