I agree with everyone who replied that each child is different, and a child can be different at each stage. For us, parents can always suggest activities, but the kids have the final say.
My DS didn't have much activities before 3rd grade, just piano, chess, and a leisurely sports activity once a week (no traveling team). Starting from 3rd grade, he wanted to get involved in various things, and we always gave him permission. My DD had lots and lots activities going on since K, she loved it. When they want to quit for legit reasons (not enough time, wanting to focus on other activities, totally losing interest, etc) we always let them. They can't quit just because something gets harder.
I did see signs of burnout for DS starting in high school because of the huge academic workload. We let him pick what he wanted to keep, but gave him our recommendations as well. I would say that any sign of burnout should be taken very seriously.
