There are two kinds of people in the world: people who answer the question "How are you?" with "I'm good" and people who send me e-mails to say how annoyed they are with all those other people.
It should be "well," these folks say, not "good."
This discussion is so common in my world that I can give an answer from memory and even cite my source from memory. My response goes like this: If you look up the word "good" in "Webster's New World College Dictionary," you'll see that, among its many definitions is "healthy." That's basically the same meaning as the adjective "well," which is commonly used to mean "in good health."
So if you're healthy and want to say so, you can choose "I am good." Of course, because the adjective "well" is more commonly used to talk about health and because so many people prefer it, it's a probably better choice. Still, "I am good" is a legitimate response to any health inquiry.