The best way to make an interesting character is giving them a big problem for them to overcome. It should be hard enough to influence the character's behavior for a long period of time, but not so difficult that it would be unreasonable or impossible (or annoying for yourself and/or other people). Ask yourself, why does the character have this problem? What would help them solve the problem? What's getting in the way of this character doing that? Once you have those answers, apply it to every aspect of your character, and let it take a stranglehold over their actions and emotions. Over time as you roleplay, you'll be able to build upon it, and either work your way towards resolving it or have your character be consumed by it.
I'll use my own character as an example. When I first started playing Ayako Kusanagi, I characterized her as a very prim and proper girl who takes being formal to its extreme. The girl grew up with the misconception that her family (one with a prestigious history) had high expectations of her and her twin sister, Ayaka; she chose to spend the bulk of her youth refining herself into a proper lady with many beneficial skills, save for any interpersonal skills (which she chose to rely on Ayaka for, as she excelled at them). To focus on her studies and to differentiate herself from the more social Ayaka, Ayako learned to suppress her emotions and expressions, which she very seldom gets passionate enough to show. As a result of her lifestyle and dependency on her sister until they moved to Karakura, Ayako never learned how to get along without Ayaka's assistance.
Now that I've played Ayako for a few years and had time for that social incompetence to simmer, I have a lot of fun playing her. She's experienced hardship in her family, friendships, and romantic relationships, all of which she (wrongly) believes to be the root cause of. Her weakened mental fortitude from her failures in relationships has caused her to begin failing in areas she used to excel, which after once believing she was a genius, dealt a serious blow to her ego. She understands that she can't go on like this forever, but has also convinced herself that change is impossible: it's too scary, too confusing, too unrealistic for her. Even so, no matter what, she always scrounges up the courage to improve herself (which is very good and also necessary if I want to actually.. y'know... talk and roleplay with people).