Compelling Characters: The Great Blogging Experiment

Today is The Great Blogging Experiment, hosted by Elana Johnson, Jen, and Alex. Visit the link to find all of the gajillion bloggers talking about this topic today. Should be fascinating to see how so many writers view characterization differently.
This is a huge topic, so I'm going to boil it down to what I feel are the basics that make up compelling characters.

I think the most compelling characters are the ones who are the most developed, the "roundest," as they often say. But those terms...