Do you care about your characters?
I think the question of whether we care - and whether readers care - is one of the most vital in all of writing. If readers don't care, they won't keep reading. If we don't care, as writers, then how can we expect our readers to care?
So how can you make people care?
It's not uncommon to hear writers talk about torturing their characters, doing bad things to them in order to make the story stronger. This is very, very important. If we don't challenge our characters, and if we make everything easy for them, then readers can quickly stop caring.
It's not enough, though, just to do terrible things. We also need other reasons to care. Something good about the person that we can relate to, or a glimpse of the character's tastes that can let us align with them. Even when dealing with an antagonist, it's useful to give them something soft and vulnerable somewhere, to keep the reader's attention riveted.
I've been watching the extended version of The Lord of the Rings, and I've been impressed over and over with how Tolkien - and Peter Jackson's treatment of the story - creates both the tender and the terrible sides of its characters. Interestingly, the extended version adds some time to the terrible events of the story, but adds far more time to the tender events of the story - Merry and Pippin dancing on the table in the Shire, for example, or Eowyn and Faramir meeting in the Houses of Healing.
The experience of depth in a story relies on the presence of both the tender and the terrible. It's a lot like dynamic range in music - a song with both loud and soft moments will leave a deeper impression on us than a song that is all loud or all soft. In fact, I highly recommend that with complex stories, you look for opportunities to provide different dynamic values for each arc that you are creating. The intimate contrasts with the epic. Action contrasts with subtle tension. Strength contrasts with vulnerability. The orcs at the doorstep of Helm's deep look frightening on their own, but they are more frightening when we are shown the families inside waiting to be overrun. Sauron is this overwhelming force of evil, but he can still feel fear, and when that fear is something that our heroes can use to their advantage, how much more interesting the story becomes! Maybe that's what irritates us so much about the Mary Sue - if she's all good, then she comes across as flat.
Some might call these contrasting elements yin and yang, or masculine and feminine - but they're more comprehensive than that. They make the difference between bas-relief and full-scale sculpture, between two and three dimensions. Either one is less effective without the other.
It's something to think about.