The last kind of electrical noise I wanted to discuss is called 1/f or "flicker" noise, and it's something of a special case. It's intrinsic in the sense that it originates with the material whose conductance or resistance is being measured, but it's usually treated as extrinsic, in the sense that its physical mechanism is not what's of interest and in the limit of an "ideal" sample it probably wouldn't be present. Consider a resistance measurement (that is, flowing current through some sample and looking at the resulting voltage drop). As the name implies, the power spectral density of voltage fluctuations, SV, has a component that varies approximately inversely with the frequency. That is, the voltage fluctuates as a function of time, and the slow fluctuations have larger amplitudes than the fast fluctuations. Unlike shot noise, which results from the discrete nature of charge, 1/f noise exists because the actual resistance of the sample itself is varying as a function of time. That is, some fluctuation dV(t) comes from I dR(t), where I is the average DC current. On the bright side, that means there is an obvious test of whether the noise you're seeing is of this type: real 1/f noise power scales like the square of the current (in contrast to shot noise, which is linear in I, and Johnson-Nyquist noise, which is independent of I).
The particular 1/f form is generally thought to result from there being many "fluctuators" with a broad distribution of time scales. A "fluctuator" is some microscopic degree of freedom, usually considered to have two possible states, such that the electrical resistance is different in each state. The ubiquitous two-level systems that I've mentioned before can be fluctuators. Other candidates include localized defect states ("traps") that can either be empty or occupied by an electron. These latter are particularly important in semiconductor devices like transistors. In the limit of a single fluctuator, the resistance toggles back and forth stochastically between two states in what is often called "telegraph noise".
A thorough bibliography of 1/f noise is posted here by a thoughtful person.
I can't leave this subject without talking about one specific instance of 1/f noise that I think is very neat physics. In mesoscopic conductors, where electronic conduction is effectively a quantum interference experiment, changing the disorder seen by the electrons can lead to fluctuations in the conductance (within a quantum coherent volume) by an amount ~ e2/h. In this case, the resulting 1/f noise observed in such a conductor actually grows with decreasing temperature, which is the opposite of, e.g., Johnson-Nyquist noise. The reason is the following. In macroscopic conductors, ensemble averaging of the fluctuations over all the different conducting regions of a sample suppresses the noise; as T decreases, though, the typical quantum coherence length grows, and this kind of ensemble averaging is reduced, since the sample contains fewer coherent regions. My group has done some work on this in the past.