While I do like to use an AP, Neutrik or similar to get hard, reliable data, I'd like to point out that for some tasks for which people would commonly wish they had an analyzer (like dialing down for minimum THD) most of us nowadays have access to all the tools needed to achieve this without spending any more money.
Let's follow the example of adjusting THD to a minimum.
Once you know HOW an analyzer does its measuring, you can think about how to "build your own".
In the days of analog signal paths and soldering components, this would be far too daunting. Nowadays however, we all have access to DAWs with previously unimaginable processing power.
A distortion analyzer first generates a clean tone at a steady frequency and sends it to an output. -This is a trivial task for a DAW.
Then it reads the return and notches out the frequency which was generated. If we generated a 1kHz tone, we insert a 1kHz notch.
Then you take the residual signal, which is all the noise and harmonics, and you have THD+N. Insert a bunch of make up gain and meter it. Listen to it too,
Using that approach, you can -for example- do a VCA symmetry trim on a DIY VCA-based compressor, and get right about as close as you could using a Neutrik or AP, but save the cost of the analyzer.
Of course, plotting graphs, measuring amplitude curves, phase curves or distortion curves would be a tedious time consuming nightmare... but for many people the ability to occasionally trim distortion or noise may be all they need.
Just musing. -A week ago I helped a friend calibrate his first ever DIY build (an 1176). When I told him how he could check THD using his Pro-Tools rig, he seemed pretty surprised.