who: me. sometimes. my cross bike has clipless (click-in whatever CrankBros on it)
why: well I didn't realize how much i like riding trails with flat pedals until I did it - your foot can be put down quickly without having to rotate it first. which is nice if you're on slow technical stuff - or you suck at mountain biking, like i do.
also, if you suck at MTBing like I do - it's easier to hop on and off to lift you're bike over logs and stuff - because you can't ride over them like a proper MTB'er. so that's nice.

major draw back - if you suck like i do at down hills - you could bounce off the pedals and not land on them again. that's just painful all over to think about. I kind of hold on to the seat with my thighs and don't go so fast on down hills.
I have come to full acceptance that I suck at trail riding, and just treat it as a nice slow ride in the woods - a Rivendell Philosophy to riding in the woods. Works great because the $50 CraigsList bike picture below is perfect for that kind of thing.

ciao.