http://www.evgschool.org/prompt_kid_on_leash.jpg <- An example
The first time I saw it, I thought it was demeaning, but then I realized it's quite practical. A little kid probably isn't going to think about it too much, and the parent probably doesn't use one because they want to equate their child with an animal. It's a way of keeping your child close, and not everyone has the benefit of never taking their kid along with them when they need to do errands/go shopping/whatever.
I was in the big mall here once and saw a three-year-old wander out of a store. I kept my eye on him, because you could tell he was just waiting for Mom to realize he was gone before taking off. He was coming toward me, so I just kept walking toward him. Sure enough, as soon as Mom comes out of the store and calls his name, he shoots off, full speed running. She never would have caught him. I stopped him with a smile and an outstretched hand, just a friendly thing, he came right to me. Had I been a predator, who knows what could have happened to this kid? Walked him back to Mom, who was crying and running toward us down the long hall. She just kept saying she couldn't stop him from wandering off, and how thankful she was I that I was nice enough to grab him, and whatnot. That kid could have used a leash, and he wasn't a 'wild' kid or out of control. He was testing boundaries. He was calm and exploring.
What does everyone else think about child leashes and the parents who use them?