Does anyone use the word "shall" in spoken English?

I do. Always have. I never realized how regularly I use it until I was a caregiver to three small girls, and the oldest started saying shall we, instead of should we. It soon caught on with the younger girls, and one day, I heard their mom say it. I commented that I thought they'd picked it up from me, and she said, "Oh, you're the one who taught them that word! I thought they got it from a neighbour kid."

There are times when shall is really the only right word.