I can only speak for myself.

In a speaker I like to look for a very fast decay rate for transparency and dynamics (cumulative spectral decay or step response show this well), phase coherence for imaging and soundstage, a smooth frequency response that extends well into the bass, wide and smooth off-axis response in the upper midrange and treble and ideally, a concentric wavefront propagation pattern. I could list more but that starts to rule out nearly every speaker if I want it that exacting to my tastes, hence I am building my own.

As for amps I am not so fussy. My experience has told me that most solid state and digital amps these days sound good to me. Low IMD is good (I seem to be sensitive to this, gives harsh highs) as is generous current ability and low odd-order harmonic distortion. I really don't mind even order harmonic distortion too much.