A good statistical model in my view should be able to answer a specific (complicated) research questions about our social world, in a relatively straightforward way. This implies answering the question of causality (see previous post) is very important in all statistical models, and second, that the statistical model should summarize our social reality in a simple way.
Proving causality can be hard and depends mainly on a good research design. Summarizing our social reality in a not too simplified way is hard, but graphics can do wonders. The video below is very old (well, 5 years), and most of you have perhaps seen it, but it is a good illustration of what I think good researchers should try to achieve (including the Swedish overenthusiastic accent).
update 11-08-2016: update of the link above: http://www.simplilearn.com/resources-to-learn-data-science-online-article