When asked, “How are you doing?” many people will immediately answer, “I am doing good.” Unless they’re talking about the good they’re doing for their community, they should have answered instead with “I am doing well.”
Good and well in the context illustrated above are no doubt two very commonly confused words. Good is an adjective (and a noun in some cases); well can be an adjective or an adverb, but in most cases, it is used as an adverb. In the example sentence, well should be used because an adverb is needed to modify the verb doing. Good is not the most appropriate word to use in this context because adjectives cannot modify verbs.
Perhaps you’ve also wondered, “What about ‘I am feeling good '? Is this correct, or is it 'I am feeling well'?” Here’s where it can get tricky. Both are correct. But isn’t feeling
a verb? Yes, but it is a linking verb. Linking verbs are different from other verbs in that they are not performing an action, but are connecting the subject with another word in the sentence. In both sentences, feeling links good and well back to the subject I. Good and well are not adverbs modifying the verb feeling; rather, they are adjectives modifying I, the subject of the sentence. Note that the meanings conveyed are different (feeling good refers to a state of mind; feeling well refers to health), but both are grammatically correct. The same is true when used with other linking verbs such as look. (You look good. You look well.) Looking good refers to attractiveness; looking well refers to health.
In a nutshell:
Good: always an adjective, never an adverb; never modifies a verb but can follow a linking verb and act as a modifier for the subject.
Well: adjective or adverb depending on context. When an action verb is involved, an adverb is needed, and well is always the choice, never good.

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Comment by ahmed — February 7, 2010 @ 5:50 pm
If “Good and well are not adverbs modifying the verb feeling; rather, they are adjectives modifying I”, then a similar line of reasoning might be applied to “taking me serious” and “taking me seriously”. Any comments?
Comment by Pieter — February 10, 2010 @ 5:11 pm
@Pieter: I’m not sure about this reasoning. I don’t think that “taking” is ever considered to be a linking verb, but I could be mistaken. Here is some additional information on linking verbs that I found:
http://grammar.ccc.commnet.edu/grammar/verbs.htm#linking
Comment by Rachel V. — February 11, 2010 @ 1:15 am