So there's the classic Lindsey Vonn-style downhill tuck. I don't think there's any debate regarding the aerodynamic efficiency of that position. I've used some variation of this to get across flats, cat tracks, or just to practice tuck turns. Cycling will get you used to getting your back low and your hands out front (unless you feel like not holding onto the handlebars...).
There's the Texas Tuck as pictured above... I figured it comes from people trying to emulate Lindsey while not having any sort of self-perception regarding how far off the "ideal" they are. I will plead the fifth regarding having possibly adopted this position myself.
And then there's what I've heard called Patroller Tucks where you don't get into a tuck at all, but you do put your hands behind your back. I've done it on runouts when you're not "supposed" to do a real tuck, but you feel like you should improve your aerodynamic profile in some fashion. Probably makes absolutely no difference, but it's still fun.