Ich bin versus Mir gehts

Can one say Ich bin sehr gut ? Or is Mir gehts the proper way. Perhaps one is less formal?

That's a good question. I'm not an expert, so Paul is the one to confirm, but what I found in searching the question is that while both are technically correct sentences, they have a slightly different meaning. In English, we make a distinction between good and well to resolve ambiguity in this kind of usage. The correct response to the question of how are you, as an inquiry to your health would be I am well in English, and in German, it should be mir geht's gut. The response to the question of are you a good person, or are you good at something is I am (very) good in English and in German the response would be Ich bin (sehr) gut.

If somebody asks you, "Wie geht's dir?" I'll confirm what Byron says and recommend that you stick with the idiomatic expressions, even if they make no sense in English: 1) Mir geht's gut 2) Es geht mir gut (this is the one that I use) This guys explains: http://germangrinds.com/2011/06/07/mir-gehts-gut/