You may be describing mollusca contagiosa, small viral warts that kids often get. These hang around for a year or so. If these have been there for years, they may be something else, such as blocked follicles. I can't think of anything serious, but you'll have to show them to a doctor in person to know exactly what they are. Before you go, tell your kids not to pop them, so the doctor can tell what they are.
Take care.
Dr. Rockoff
It sounds to me like Keratosis Pilaris. You can Google it for more info. I've had it for years and didn't know it until I saw a product on Sephora.com that was supposed to help it. The prduct didn't work, but I got a lot of information here...
http://www.helpforkp.com/keratosis_pilaris_about_kp.html
I don't advise trying the Derma Doctor product advertised - KP Duty, I think it's called. It's expensive and didn't really help much.
Long story short, it's harmless, but unsightly.