Just took a look at http://blog.notdot.net/2009/11/Damn-Cool-Algorithms-Spatial-indexing-with-Quadtrees-and-Hilbert-Curves . Their discussion of Hilbert gives a nice taste for why someone might care about Hilbert curves.
It reminded me of a recent paper published by Eric Lander and colleagues regarding the folding of the human genome. Long story short, it is a real-life Hilbert curve. The upside to this is that Hilbert curves untangle very easily, allowing for relatively easy access to deeply buried regions. ( http://www.sciencemag.org/cgi/content/abstract/326/5950/289 ) Perhaps most importantly,it made for an attractive cover on Science Magazine.
