Actually there is a minimum operating Voltage. That is what you need to actually be able to open a transistor gate, and was around 0.6V or so, if memory servers me correctly. I recall an article in Wikipedia mentioning that, it was called Threshold Voltage. I also recall experimenting with that during 2010 with a massive undervolt and underclock of a Deneb RB-C2, and wasn't able to get under 0.6V.
http://imageshack.us/a/img694/6695/undervolt.jpg
http://imageshack.us/a/img693/7742/undervolt2.jpg (Imageshack resize seems to have killed it)
http://imageshack.us/a/img696/5256/undervolt3.jpg
Current Power Saving techniques are based on shutting down parts that you don't need instead of making them work at minimal Frequencies. I still think that a massively underclocked and undervolted Processor may be useful if you want to keep your computer on because you like to leave all your Instant Message applications, uTorrent, etc, open and ready to use. Power consumption from the Processor itself will be minimal in such state. But its the rest of the system power consumption what kill the power efficiency of doing so, not the Processor itself.
There is actually a technology called subthreshold computing where one uses the subthreshold current (leakage) to do useful work.
There is another field of study referred to as near threshold computing which is also quite cool.