Besides the coolness of creating non-volatile, solid state memory, being able to hook up these very small memristors to make really small transistors could be another way to keep Moore's Law "true".
edit: See the Wiki here with several references:
http://en.wikipedia.org/wiki/Memristor
edit2:
Nature subscribers can find the recent paper here:
http://www.nature.com/nature/journal/v453/n7191/full/453042a.html
The prospect of using them to create an artificial brain is most interesting. I've read about a project where the researchers are actually modeling a neuron (
http://www.seedmagazine.com/news/2008/03/out_of_the_blue.php ) on a chip. They have 2,000 such "chip" neurons running now simulating a slice of rat brain.
Super-small transistors built from memristors, with their special properties, could be the
missing link (had to keep the theme going!
) to artificial brain projects.
Best,