Over three decades ago, the memristor was theorized as the fourth basic passive electrical element, to go with the resistor, the capacitor, and the inductor. The memristor Wikipedia article explains it better than I can. HP Labs just discovered that some nanoscale switches act as memristors.
We already know of one practical application: They could provide RAM-like speeds but be non-volatile, keeping their data while powered down. According to some of the comments in the /. article where I read about this, they could also simulate a transistor at smaller than what we have now, and it could be used as analog memory, which may have some AI uses, among others.
In any case, it sounds like there will probably be tons of applications for this that we haven't thought up yet. I don't know how far out commercialization is for any of this, but it's still a great reason why science research is important.
Update:: Ars Technica has a nice writeup that describes how HP's memristor works. It also shows the symbol for it, which apparently looks like a square wave (whereas the resistor's symbol is a sawtooth wave).