JOEL - I don't think so. I have a friend in my ward who is an 82 year old widower and they still let him go to the Single Adult dances :-)
Oh, you are probably talking about younger kids. It depends on if you are talking about church sponsored dances or any kind of dance(like a school dance).
As far as church sponsored dances are concerned the Church handbook says:

"Youth under 14 do not usually participate in youth conferences or dances that are held at times other than the regularly scheduled Mutual night"

This is mostly up to the Bishop as to what age group can participate in these dances.
As to other dances outside the church, the age restriction is pretty much left up to the parent of the child. The church has advised the youth to not date until they are at least 16 years old. But I believe that most LDS parents stick with the age 14 limit when it comes to going to other dances. Some let them go younger if they feel they are mature enough for it.