Noise is an omnipresent challenge for designers of most electronic circuits, and especially so for the analog ones. Of course, you could look at it from a reverse perspective and argue the opposite: Without noise, many designs would be much simpler to implement, and fewer experienced, skilled engineers would be needed (so perhaps engineers should stop complaining about it?).
Regardless of where you are along the noise love/hate relationship spectrum, it's important to remember that this simple word actually represents many diverse forms. We can classify noise by either its source or by its characteristics: In the former group, we have motor noise, atmospheric noise, thermal noise, internal noise, and external noise, to cite an overlapping few; in the latter group, there are white noise, pink noise, impulse noise, narrowband noise, non-additive noise, and many others. When in doubt, you can even cite EMI/RFI, which is a broad-brush label for noise which can take on many forms.
Why all this thinking about noise? Planning how to deal with it and then executing these plans often occupies a significant amount of design and debug time. It usually requires a blending of techniques such as shielding, filtering, clipping, and blanking, all done in the analog domain, as well as a wide range of noise-reduction algorithms which are implemented in the digital domain, and which can take up quite a lot of the processor's resources (plus up-front programming time).
That's why the more you know in advance about the noise source and type, the better you can do with managing it. It's easy and simplistic to assume it is AWGN (additive white Gaussian noise), but that is often not the reality. So why assume white noise? To start, there are many tools, techniques, and tricks for dealing with it, so it's certainly a tempting assumption. However, designing a product to deal with white noise when the noise is really has impulse characteristic or is due to a nearby transmitter, can be a big mistake.
In his classic work Detection, Estimation, and Modulation Theory, Harry L. Van Trees emphasized that there is a hierarchy of challenges in signal demodulation and processing. The easiest case is known signal in known noise, such as an AM radio broadcast signal with white noise; in the middle are known signal/unknown noise and unknown signal/known noise (where an "unknown" signal is one about which little is known in advance about its format, modulation, or other characteristics); and most difficult is unknown signal in unknown noise, such as intergalactic emission.
Most engineers have a noise type they respect and perhaps even fear most for the challenges it brings, or a favorite they like to talk about. One of my favorites is cyclostationary noise (see here and here), which is white noise but with a mean which is periodic and with a defined cycle. It's actually a fairly common type of noise, seen in the physical rotation of a motor bearing or a non-fixed radar antenna (not all radars used phased-array topologies), in radio astronomy (as the Earth rotates), or in electronic components (such as within some oscillators and PLLs). On one hand, cyclostationary noise is AWG-like, the easiest to analyze in time and frequency domains; on the other hand, the cyclic nature means that it is more complicated than AWGN and any noise-reduction scheme has to be dynamic and perhaps even synchronized, as well.
Stationary noise with an arbitrary PSD is modulated by a periodic signal. This is representative in both ways in which cyclostationary noise is generated with modulated noise sources and modulated signal paths.
(Source: "Noise in Mixers, Oscillators, Samplers, and Logic: An Introduction to Cyclostationary Noise" by Joel Phillips and Ken Kundert, Cadence Design Systems as published in Custom Integrated Circuits Conference, 2000. CICC. Proceedings of the IEEE 2000)
A good engineer doesn't fear the noise but instead embraces it and becomes "one" with it, because there is no alternative to dealing with it and overcoming it. To paraphrase a common saying: You can run from it, but your design can't hide from it.
What noise types have you dealt with? What noise gave you the most difficulty? What was the most unexpected noise you have encountered?