Great post, and thanks for serving as a science fair judge.

The question of how to rank things has some interesting statistical issues when the ranks are based on multiple scores (for example, scores from different judges). In most cases, I advocate including confidence intervals for these kinds of rankings. See http://blogs.sas.com/content/iml/2011/03/30/ranking-with-confidence-part-2/

There are also statistical ways to find "the cream" and "the dregs" without ranking. Funnel plots are one idea that have received a lot of attention lateley. See
http://blogs.sas.com/content/iml/2011/04/15/funnel-plots-an-alternative-to-ranking/

Of course, neither of these solve the "blue ribbon problem": People WANT a ranking, even when there are no statistically significant differences between some of the participants. No one wants to hear that little Susie's project is ranked between 2 and 4, with 95% confidence. Judges use their experience, opinions, and gut feelings to break ties, and little Susie and her friends learn that life is not completely objective.