I actually just started minimalizing drastically in this area....I've cut down each child's shoe collection to 2 pairs -- one pair closed-toe sandals (Keen or Merrell) and one pair casual dress shoes. DD has an extra pair of dress sandals/Mary Janes because she wears dresses to church a lot. That doesn't count rain/snow boots.
It was extreme, especially for me because I'm a shoe girl. But I was just getting SO sick of having to trip over their shoes and everything. I'm making myself stick with this for an entire year and then I'll see how it went and adjust their shoe collection from there. It's been going really well so far.