So how are you to reply when someone asks you how you are: I’m good? I’m well? We hear them both, but we know that our ears are not to be listened to in matters of grammar; what we hear is only as reliable as the people we listen to. The answer is that both replies are correct, but one is saying something about your health and the other about your moral stature.
I harp a lot on how practical a little theory can be, and the question before us here is a good illustration. The apparatus of grammar classifies good as an adjective, a word that describes a noun by naming some quality it possesses. An intelligent person has the quality or essence or nature of intelligence adhering to him or her; a tall building displays tallness, and a crazy uncle has taken on some measure of craziness. The term adjective means thrown at or attached to, and this derivation points to the idea that adjectives name applied qualities: someone who is talented is someone to whom some amount of talent has been attached, whether by birth or hard work or both.
The word well, on the other hand, is an adverb, that part of speech which modifies a verb, not a noun. While adjectives name qualities that have taken possession of something, adverbs point to (among other ideas) the manner in which something is existing. To say that the dog is barking loudly is to say that what is loud is not the dog but the barking. The adverb loudly is indeed built from the adjective loud, but it points the reader’s attention not to the noun, the dog, but to the verb, is barking, and the manner in which that action is occurring. Verbs are not things to which qualities can adhere, so adjectives cannot modify them. Adverbs, though, can involve themselves with verbs (the word verb is right there in the term adverb), and in so doing they amplify the circumstances in which something acts or exists. In revising our work, it can be very helpful to remember that adverbs answer one of five questions: where? when? how? how much? or why?
These five adverbial questions, moreover, can help us understand how to answer the million-times-a-day-asked question How are you? The interrogation begins, after all, with the adverbial question how?, so the speaker is really asking In what manner are you existing?, to which the grammatical reply in standard English would be I am well (and if you went so far as to answer I am existing well, you would be marking yourself as someone who has spent too much time reading philosophy). On the other hand, if you answered I am good, using the adjective instead of the adverb, you’re still speaking standard English, but for some reason you have decided to ignore the speaker’s question and suddenly blurt out that you are a good person—because the adjective good is naming a quality, a moral quality, that has stuck itself to the subject—you. Happily, you are on the road home.
Just what standard English is can be debated unto the end of time (and that debate should begin with the assumption that language is always on the move and ever changing), but the term standard English refers in good part to the practices justifiably acceptable to those who worry about the integrity of language—that skill, or art, which helps us divine just what is going on inside our minds and bring it before someone else. The keepers of language are alive to the fact that the instrument of language can be easily dulled, that we can fail to make distinctions and, worse, fail to realize we are failing. Intelligent writers and speakers understand the place and purpose in which they find themselves, and use language in a way that accords with that moment. To throw the rule book at someone is foolish, but not to consider accepted procedure is equally unsmart. A middle course is best.