one of those simplistic yet important songs in pop music, I got to watching some youtubes of them doing the song in '66, and recently; ..strikes me that the singer (Rudy?) is a very Stones-y dude. I've always liked it, and the style, Tex - Mex or whatever..
The song [but not the ? and the Mysterians version; it was a low-budget film and Allen Klein's price was likely too high, as was the song by The Police] was used in the 1985 film Cat's Eye, an anthology of shorts based on Stephen King stories. In case you haven't seen it, here's a little set-up for the scene below. Alan King plays a counselor for a mob-run clinic for smokers wishing to quit. They are forceful in their methods, and because James Woods has fallen off his nonsmoking regimen, they bring his wife in to be tortured. The song 96 Tears is played as she cries, well, 96 tears:
Yes it's amazing that ? and the Mysterians are still going today, with most of the original members present.
Don Was once posted on his Wasmopolitan Cavalcade website a great version of "96 Tears" from one of the annual Concert of Colors by ? who was backed up by an all-star band of Detroit musicians. That was my introduction to ?. I recommend you look for it on the web.