A neggitive impedance reduces its resistance as the current increases instead of remaining constant, this means that if the current is increased the voltage across it won't increase proportionally as ohms law normally states and in some cases can cause destruction of the componants.
Examples of negitive impedances are:
Electrical arcs this includes discharge lamps (neon, flourescent, sodium ect.).
Transistors, eg. output stages of class AB amplifiers.
Negitive coefficient thermistors.
Diacs.
Zener diodes.
Diodes.
LEDs.
The first two have the desructive properites I described before the current is limited with a ballast inductor or resistor with discharge lamps and purly with resistors in amplifier output stages. Results from experiment I've conducted indicate you can (despite what some people say) power LEDs from a constant voltage source but it has to be exactly the right voltage for the forward current you require and this is totally differant for each LED even if they have the same make/model.