IMHO, "Who am I?" would be used when you introduce yourself, usually posing the question to the very person/people who you want to introduce yourself to, but immediately following it up with an introduction.
Person A:"Who the heck are you?"
Person B:"Who am I? I am the Supreme Ruler of the Universe."
Also, if you are unfortunate enough to lose your memory, you would be asking yourself(or the people around you) this question!
And, when you ask "Who I am?", the emphasis is on the "I". Thus a person will use it in a situation where he would want to highlight himself. I think its use is mostly rhetorical.
Person B: "How dare you laugh at me? Do you know who I am?"
Person A: "Uhh.. The Supreme Ruler of all the idiots in the Universe."