What determines whether or not to use the crush washer supplied with spark plugs?

tapered (45 degree or so) seat plugs do not include or need a washer.

Flat (90 degree) seat plugs need it and come with it.

Common older heads use short reach flat seat plugs with a 13/16 hex and a washer.

most newer heads use a "peanut plug", 3/4 reach, 5/8 hex, tapered seat, no washer.

Thanks.

One thing I thought I'd mention is if you're putting spark plugs in aluminum heads always put a little anti-sieze on the threads. It's a life saver.