I would say, their personality. Not just their personality but also their flaws, their weaknesses. But most importantly is that none of the characters in your world should be able to get off scot free when they have done something wrong. Or are not excluded from repercussions.
And for me, I liked watching my characters suffer through things. Watching every bit of their lives eventually impacting them and peeling back all those layers. People are three dimensional, and everything they go through would affect them in some way or another. As a writer, it’s knowing how it would affect them and portraying it as such. Rather they would become bitter, ir at least a little kinder or taking on any traits. But they must learn something by the end of the book.
And another is having them fail horribly only to pick themselves up. That is true strength, not badass abilities like swordsmanship, knife throwing, or some abilities which makes them only physically badass. I also like verbal ones too.
And unlike protangists this has to apply to all characters in the story. Either minor ones, supporting characters, they all have to impact the story in some way, and likewise.
Most importantly, it’s also being able to relate to their characters. I also enjoy books based on how relatable they are, rather than just on the interesting personality. Sometimes it can be hard to relate to some characters but their characters are interesting, but not entirely plausible based on the background. Backstory also gives depth to them, but their current personality also has to reflect what they went through, and how it impacted them. The backstory has to explain what made them as such, and not just there to induce tears. There is a relationship between these two, and sometimes the backstory simply doesn’t explain why is a character so.
As some backstories can be abosrbed by different characters with a complete turn in their personalities. It can also explain some of their quirks, and also some of their behaviour. But both must reflect each other and give a very very plausible explanation for it. Different people deal with problems differently and their age can be an issue too. Ultimately, I read books and expect backstory which gives a character necessary depth, instead of contradicting their personality itself.
So, what do you think on this? I really would like to hear your input based on this issue.