With the fosters, if I have time, I do teach a "Stay" because most adopters will expect it and so the pup might as well know what it means.
With Pongu I initially taught "Stay" as a separate command for the same reason that I initially did not teach an automatic Sit at Heel when I stopped -- because we were training in freestyle at the time and you do things a little differently in that discipline to get a smoother-flowing routine.
Currently Dog Mob does not need a separate "Stay" command, they just hold position until I tell them to do something else. Sometimes I give it anyway for clarity though; it's basically a secondary cue that I sometimes find helpful as a reminder under stress. "Wait" is a separate thing to them; it basically means "do not pass this doorway until I say you can, but you don't have to hold a particular position in the meantime."
I'm working on getting Pongu to Stay during heeling when I lead off with my right foot and come with me when I lead off with my left foot (i.e., standard competition obedience footwork) but we're not there yet.
ARCHMX TDCH Pongu the Insane, CD-C, RE, RL1X6, RL2X5, RL3X2 (GSD mix, b. Apr 2010)
Crookytail the Tigerwuff, RL1, ITD (Akita mix, b. Jan 2011)