This question - asked so often - suggests that there is actually a plausible answer. Almost as if our being were a fixed thing. People who ask this sort of question are typically struggling with their identity and are searching for a core sense of themselves. The irony is that the more you seek to identify who you are, the more fragile you are likely to feel about yourself. There may be an inverse correlation between the question being asked and the ease with which you experience your life. The emphasis shouldn't be on discovering who you are (what is buried beneath) but on facilitating the emergence of what you'd like to experience.
Our identity should be seen as an ongoing process. Rather than a static snapshot, we should embrace a flowing sense of self, whereby we are perpetually re-framing, re-organizing, re-thinking and re-considering ourselves. How different would life be if rather than asking who am I, we contemplated how we'd like to engage life?
A sense of inadequacy often informs the question around "Who am I?" As people engage the deepening complexity of understanding themselves, they would fare much better to devote themselves to the unfolding process of life. Witnessing our thoughts, not reacting out of old habit, and becoming present enable us to better craft our lives. As such, the identity that we seek fires the wave of life, enriched by the flow.
Imagine that you've been in prison for twenty years, incarcerated since the age of eighteen. You literally have no adult life experience outside of the penitentiary. Your sense of self is tragically limited. You might ask yourself, "Who am I? This would likely provoke a fragile sense of self that paradoxically might leave you most apprehensive about your imminent release. You'd hardly choose to remain imprisoned until you could find your identity. You'd have to permit that new sense of self to flow from your new experiences.
I have worked with people who have been married more or less for their entire adult lives. Upon divorce they are often confronted with a distressing thought. They claim that they don't know who they are. More to the point, they may not know who they are as a single, autonomous adult, not partnered. After all, how could they? Rather than remaining mired in fear, you'd need to summon up a sense of wonder and adventure. There is a new sense of self waiting to be born. You get to re-craft yourself along the way.
At the other end of the identity continuum are those who claim to know themselves so well. This other extreme also signifies a fragility about one's identity. To know yourself so well leaves no room for growth. Even more, it suggests a deep vulnerability that is being defended against - as if it were too dangerous to take a closer look.
It makes perfect sense to seek a deeper sense of self. To become intimately aware of your thoughts, feelings, hopes and fears is obviously advisable. The key is to engage your sense of self as malleable, more like a willow tree than a sturdy oak. The willow is flexible and survives the storm as it bends with the wind, whereas the more rigid oak is more likely to crack.
The universe purportedly exists in a state of flowing potential. And it is essential to understand that we are indeed part of that universe. The goal then is to access that potential, keeping the parts of our identity that continue to serve us well and shedding the old, habitual pieces that constrain us. This process is known as positive disintegration. This permits us to find balance between the extremes previously discussed and enter into a relationship with self that commits to our personal evolution.