"No, I'm good" is a casual way to say "No, thank you." You use this phrase when someone offers you something, like food, drinks, advertising materials, etc.
"I'm good" sounds friendly and casual. You can use it with friends, coworkers, waiters, and most other people.
A couple of occasions when you would not use "No, I'm good" are:
- You're meeting your girlfriend's parents for the first time, and you're not sure if they like you yet.
- You're very angry at your coworker because he blamed one of his mistakes on you to your boss. Now he's going out to get coffee and asks if you want any.
In these cases, "No, thank you" would be better.