Have never used them, or felt the need to use them with Shimano cranks and SPD pedals. If supplied, or recommended then I would use, but I wouldn’t use them just for the sake of it.
The instructions for both the latest and previous generation of Shimano pedals make no mention of washers. Nor is one included with the latest XTR chainset.
I suppose other manufacturers will vary their recommendation, but for Shimano I would say it’s a solid “no”. Personally, I would say it’s more important to keep threads greased and torque the pedals up correctly. If your pedal is chewing up the crankset, then it’s probably not secured correctly and nothing writes off an expensive set of cranks quicker than loose pedals…
Edit: Note that SRAM’s official road and track crankset manual does mention pedal washers, so you probably want to bear this in mind too… (pages 19 and 24)