We started off doing smoothies with fruit and yogurt about 8 years back. We loved them but besides carrots we never considered using other veggies. For about 3 years now we are using all kinds! You can add sugar (we don't) or honey (don't do that either) it helps if you or your children are not real veggies lovers.
I prefer to use a blender and don't like using juicers anymore, I think we need all that fiber that they just separate and you end up tossing to the compost, goats or garbage.
Fresh Baby Carrots
Fresh Celery Stalks
Blend up with water and drink!