I usually clean up after the dog -- I make it a rule to do it. I have reasons:

First, dog feces are a barometer of my dog's physical condition. Since I'm not a doctor, one of the things I can do to make sure my dog (or cat) is in good health is check her feces. Feces tell me a lot of things with their color, firmness, smell, size and so on. I take the condition of feces seriously because my pets cannot tell me verbally how they're feeling physically.

Second, picking up after the dog helps avoid spreading parasites like roundworms and tapeworms. Children can pick up these parasites while they play outside, and so can adults if they walk around outside bare footed. Such transmissions can be avoided or at least kept to a minimum when feces are picked up.

Third, I don't want to step on dog poop! I don't know how many times I've stepped on poop when I walked my dog in the park or in the street. Yuck!