Sometimes I look to what my favorite archetypes are, and try to put a new spin on them. Or simply take ideas from stories you have read or like and make them your own.
I like watching perfectly good characters become corrupted over time, so I have several of those in the planning stages of my story. Or having characters that are hiding secrets from other characters that could be catastrophic when revealed.
When I make my characters, I already know what roles they have and what important events occurred in their lives. I focus on smaller events and explain parts of their personality. Sometimes I make characters based around a motivation or idea and make a background that expands on it, though, I usually use it for groups. Listening to music helps a lot. Occasionally, I get inspiration from a song, anime, or something like that and it just flows out. After I'm done the first time, I go over it again and add or get rid of some things.
It sounds weird, but I let my characters tell me. Inspiration hits, I draw them, and as I draw more of them, I start to learn more about them. I've never really sat down and tried to think of a past for any of my characters; it ends up unraveling as time goes on and I draw them more and think about their person in general.
Work out how you need them to be in the story, and then you can work out how they got like that. E.g. One of my characters was very boring so I figured I would give her a rebellious streak. So then I thought about what in her past and personality would have made her that way.
Backstories can also provide motivation for your characters, so you can think about what your characters need to do in the story, and then think about what in their past would motivate them to do that. Another of my characters has money as a motivation for getting famous. So I gave him a backstory of coming from a poor family who nonetheless supported his dreams, so he wants to be successful so he can support them financially to repay them.
I actually have a random roll chart, that takes a 10 sided die for example
1 - both parents living and togehter
2 - both parents dead
3 - father alive/mother dead
4 - mother alive/father dead
5 - both parent alive, seperated
6 - never knew parents
7 - both parents living and togehter
8 - both parents dead
9 - father alive/mother dead
10- both parent alive, seperated
And a chart for a few years of history, with good things and bad things that can happen. How many brother and sisters they have. What they treasure most. Come up with a new one any time I am stuck creating charachters. I totally stole this idea from the RPG game cyberpunk and their random roll charachter chart.
Look at your characters. Observe how they dress. Question why they dress like that and go farther with it. What's their personality? Why do they behave that way? What do they like, and why do they like it? Stuff like that helps me a lot when writing backstory.