One of the best, if not the best, books of philosophy of the modern age is The Mind's I: Fantasies and reflections on self and soul, edited by Douglas R. Hofstadter (of Gödel, Escher, Bach: an Eternal Golden Braid fame) and Daniel C. Dennett. This work is not some dry scholarly dissertation; it is a collection of 27 different writings on a common subject, ranging from scholarly essays to works of science fiction to parables, along with attached comments by the editors.
Together, they comprise a tour de force examination of the question of identity -- when you refer to yourself, to what exactly are you referring? Along the way related topics are addressed, ranging from the unity of the organism to soulism and the relationship of mind to brain, to theories of intelligence and the question of artificial intelligence (including John Searle's infamous "Chinese room" analogy), to epistemology and the question of perception and perspective, to some of the central tenets of transhumanism. Defining works by such greats as Alan Turing, Richard Dawkins, Jorge Luis Borges, Stanislaw Lem, and Raymond Smullyan are included and analyzed as parts of the puzzle. All sides of these questions are examined.
So thorough and informative and entertaining is this book that it is hard not to start any discussion about any of its subjects without telling people "go read that book first", since it sets up such a thorough grounding in all sides of the various issues tied up in this common theme, and without that, almost any discussion ends up mostly retreading parts of the book.
There is a danger in recommending the book too highly, though. I've had to buy it three times, since the first two copies were borrowed and never came back. So buy your own copy! If any of these topics interest you, you will not regret it.