Indeed, as Win says, you can get some signal out of a diode detector
even for very low input levels. With fairly simple home-brew
techniques but a lot of attention to the details of leakage currents
and op amp offset voltages, I'm able to detect RF signals down to a
very few tens of microvolts. That's using either a zero-bias Schottky
detector diode such as the Agilent HSMS-2860, or an old germanium point
contact diode. At very low signal levels, the optimum load resistance
is quite high. (See Agilent detector diode ap notes for details.)
Things are actually easier if you're only interested in the modulation
component of an AM signal, and not in trying to detect the carrier
level, since the offsets aren't particularly important for AC signals.
A JFET audio amplifier, or even a carefully-designed bipolar amplifier,
can give you a very low noise figure for the high source resistance
that the diode detector running at low input levels gives you.

There are tricks you can play to make a receiver that works from the
power received by the antenna. If you live near a transmitter that's
putting out significant power in your direction, you may be able to set
up a rectifier for that received power and use it to run a micro-power
amplifier following the detector for the station you wish to receive.
If you want to hunt for weak stations, you'll need a carefully designed
and built RF input tank/filter circuit. At night, especially, it's
possible to listen to stations quite a ways away using no active
components in the RF path before the detector.

Cheers,
Tom