The importance of low ESR/ESL caps in analog circuits can be debated.
Used in coupling, there is no doubt that ESR/ESL is utterly negligible compared to the impedance of the circuit they are used in.
For example, a stage with an input impeance of 10kohms should use a coupling cap of at least 8uF (for less than 0.5dB attenuation at 20 Hz), but due to their higher non-linearity, electrolytics should be at least 5 times larger. So a 47uF should be used. The typical ESR of a standard lytic 47uF cap is less than 1 ohm (typically about 0.2). It is clear that apart from the marginal attenuation (less than 1milli dB) there is no effect.
Where it makes sense to discuss the subject is decoupling. Because of the impedance of the supply rails, the decoupling caps have the task of maintaining the correct voltages in case of demand.
It is important to distinguish between sudden demands, created by transients, and more steady demand created by high amplitude LF signals.
In order to react quickly to a sudden demand, the supply must have a very low series impedance, that's why it takes low-ESR caps, such as ceramic and short lines, and also why the ceramic caps must be placed close to the stage they are decoupling. In addition, the return current from this stage should be returned as close as possible to the reference point ("ground") of these decoupling caps.
For example, if this stage drives an external load, this load should be returned to the decoupling caps reference point, rather to a convenient (but inadequate) star point.
Regarding low frequencies, the length of supply lines/traces does not matter that much, so it's quite common to have only one point where lytic caps decouple rails. Due to the much different demand (continuous LF) these decoupling caps should be dimensioned according to the output requirements. When a pair of 47uF caps is enough for a circuit that drives a 10kohm input, much larger values are required for driving a 600 ohm transformer. The same rule applies, when driving an external load, it should be returned to the reference point of the decoupling caps, which may not be exactly the stage's reference point.
Back to the point: what about ESR/ESL?
The actual impedance of the rails reflects as how much the supply rail drops when submitted to a current demand.
The consequence is how much this voltage drop reflects on the output signal?
The answer is PSRR (Power Supply Rejection Ratio). When opamps have a typical PSRR of 100dB - meaning that a voltage drop of 1V of the supply rail results in only 10uV at the output - , a basic common-emitter stage has zero PSRR, so using a low-ESR cap makes perfect sense.
The situation with opamps (whether monolithic or discrete) is a little more complex, because the wonderful 100dB PSRR is valid only a LF, falling down to about 50dB at 20kHz.
That summarizes the need for large capacitors accompanied with their inevitable ESR, complemented by local low-ESR caps.
Is there a significant benefit using low-ESR caps for the larger ones? Some think there is, which makes them use large film capacitors for this task.
I have not seen a proof of increased performance resulting from this choice, however there are reports of impairment, due to the combination of trace/wire inductance and capacitance which result in a high-Q LC circuit in series with the supply rail and resonating in the audio band.
Member ricardo has a lot to say about this.
Of course, requirements for high-speed logic and RF circuits are different.
