Jeff, Silicon transistors require about 0.7 volts to turn them on, so I think that designing a radio to operate at below 1 volt or so would be difficult.
Several small pocket portables use only
one cell, that is really the lowest
practical limit.
The smallest AM/FM pocket radio with speaker that I have (S0ny ICF-S11W) uses 2 AAA cells:
But getting back to the intent of the thread, here is a S0ny AM/FM/SW Multiband radio (ICF- SW1), shown next to the S11W... It uses 2 AA cells for power, as well as a wall-wart and is a decent performer on SW.
jr