It is necessary to separate reasonable extrapolations and speculation about mind uploading from the magical thinking surrounding it. Several metaphysical questions are brought up by the prospect of mind uploading. Like many such questions, these may not be objectively answerable, and philosophers will no doubt continue to debate them even after everyone's been uploaded into computers.
The first major question about the plausibility of mind uploading is more or less falsifiable: whether consciousness is computable in its entirety. In other words, assuming that consciousness is not magic, and that the brain is the seat of consciousness, does it depend on any special functions or quantum mechanical effects that cannot ever be simulated or computed by other hardware? This question, of course, remains unanswered, though considering the current state of cognitive science and brain-computer interface technology, it is not unreasonable to think that consciousness will be found to be computable in the future, despite the claims of non-materialist neuroscience.
Assuming that consciousness is proven to be computable, the second question is whether the "strong AI hypothesis" is justified or not: If a machine accurately simulates a human consciousness, such that it passes a Turing Test or is otherwise indistinguishable from a natural human being, is the machine really conscious, or is it a soulless mechanism that merely imitates consciousness?
Third, assuming that a machine can actually be conscious, is a copy of your consciousness really you? Is mind uploading really a ticket to immortality, in that "you" or your identity can be "uploaded" to a computer?
Dualists would hold that it's impossible to transfer a consciousness from a human body to a machine: A simulation of a person would only be a copy of the original; a new consciousness with implanted false memories. The machine may believe itself to have the same identity as the original human, but the soul or immaterial mind of the original was lost when the original body died, so it is not in fact the same identity. With this approach, mind uploading would simply create a computerized facsimile of your conscious functions. The philosophical problem with uploading "yourself" to a computer is very similar to the "swamp man" thought experiment in which a clone is made of a man while the "original" is killed. Just replace "clone" with "uploaded mind." This is one reason that has led critics to say it's not at all clear that the concept of an uploadable mind is even meaningful.
Advocates of mind uploading take a more pragmatic approach, defining human identity based on memories and personalities rather than physical substrates. They believe that the copy of the mind holds just as much claim to being that person as the original, even if both were to exist simultaneously. When the physical body of a copied person dies, nothing that defines the person as an individual has been lost, so they are in fact immortal.
Like the Ship of Theseus, all the atoms in our bodies are replaced by new ones on a yearly basis, yet most people agree that we retain our identity. If the atoms are replaced by simulations of atoms, which otherwise function identically, what's the difference? Is a copy of a book "the same book" or "a different book"? It depends on which aspects of the book are important in the context of the question. If you consider the words to be the important part of the book, then they are the same book. If you consider the physical binding to be the important part of the book, then they are different. In the context of mind uploading, the physical computer that the consciousness runs on it is unimportant; all that matters is that the memories and personality of the individual are preserved. As the recently-murdered protagonist states in Down and Out in the Magic Kingdom, "I feel like me and no one else is making that claim. Who cares if I've been restored from a backup?"
 See also
- Collection of articles on mind uploading
- Welcome to Life - The Singularity, Ruined by Lawyers.
- Against Naive Uploadism: Memory, Consciousness, and Synaptic Homeostasis, Seth Weisberg, H+ Magazine
- Why Transhumanism Won't Work, The New Atlantis (A misleading title, the article is about mind uploading, not transhumanism in general)