Circuit elements composed of certain materials exhibit the property that, over certain voltage ranges current is a decreasing function of the voltage. This range of voltages is known as a negative resistance region.
It may be more correct to say that a circuit element has a negative differential resistance region than to say that it exhibits negative resistance because even in this region the static resistance of the circuit element is positive, while it is more precisely the slope of the resistance curve which is negative.
An example of an electronic component exhibiting the negative differential resistance region is the tunnel diode. Such a device, when biased into its negative differential resistance region, will act as an amplifier.
In conformance with the known law of conservation of energy, a plot of the negative differential resistance region of a component cannot normally pass through the origin.
More recently however, Professor Deborah Chung at the University of Buffalo has discovered a composite configuration of carbon nanotubes which actually does exhibit a negative differential resistance region throughout its entire plot, which does indeed pass though the origin. Professor Chung's device could thus be considered a negative static resistor.
Another concept of negative resistance exists in the domain of radio frequency antenna design. This is also known as negative impedance. It is not uncommon for an antenna containing multiple driven elements to exhibit apparent negative impedance in one or more of the driven elements.