The traditional distinction between good and well is that good is an adjective describing something as pleasing or of acceptable quality and well is an adverb meaning the action is done in a pleasing or acceptable way. However, both good and well work as adverbs in informal speech and writing. A caveat to this is that well can also be an adjective and means that something is healthy.
If someone asks, “How are you?” It is grammatically acceptable to answer, “I’m good.” Answering, “I’m well,” is also acceptable, but carries the connotation of not being sick.
You might want to read about the interesting phrase “Fair To Middling” here.
Examples
After receiving several badges and medals for expert marksmanship and good conduct, he officially retired from the military on disability in December 2012. [New York Times]
So for a well-loved chief executive, a manager, and so many good players to leave the club in the space of a few months constituted a meltdown. [Daily Mail]
If I’m good enough to play in this league, I want to do it. If I’m not, I’m going to play somewhere else. [NJ]
“I’m well enough to work two days a week. I really should not be here, but I’m sitting here as proof this treatment works.” [Sun Sentinel]
Meredith had six weeks off after being hospitalised, before returning to umpire in round 21 and has performed so well he has won the coveted position. [AFL]
I’m well aware of what they did to provide for my family and what my mum still does, and this is my chance to add to the story. [New Zealand Herald]