Is there an electrical component such that its impedance has a negative real part ?
Fact: Any electrical component made from resistors, inductances, capacitors (connected in possibly complex ways using series or parallel connections recursively) must have an impedance of a non-negative real part.
Proof: Suppose that there exists a way to connect the components (R,L,C) in a possibly complex ways using series or parallel connections recursively to get an impedance with a negative real part. Choose the connection of R,L,C that uses the least number of connecting wires. Let's call this component COM.
Best Answer
Using simple devices L's, C's, and R's by themselves, you cannot get a negative resistance. It takes either an active device (see Scott's answer) or some physics happening in an individual device.
There are at least three primary devices that hold historical significance that have this characteristic which are the Back diode, the Gunn diode and some tunnel diodes.
All of these devices have regions of their I-V curves that exhibit negative resistance. You must bias the signal to span these regions of interest and not go beyond. Here is a snip from "American Micro Semiconductor
The back diode was used for envelope detection in early radar speed guns.
The Gunn diode operates on a different principale and is called a Transferred Electron Device (TED). These are typically used in oscillators, when paralleled with a device of opposite characteristics the combination oscillates at millimeter wavelength frequencies.
Here is a semi-complete list of types of devices that all have negative resistance; (Source: - Complete guide to semiconductor devices by Kwok K. Ng);