If you could upgrade yourself, would you? How far would you go? Would you get an artificial heart that means you have no pulse? Are you still human? What if you get a hearing aid now? What if you break your bones and have metal rods inserted into you? What if you have a genetic disease and undergo viral therapy to cure it, literally rewriting your genome? What if you have hair implants?
Some of these artificially mimic the human form, and others go beyond it for the sake of your own livelihood. If science progressed to the point that you could never be sick again, would you still be human without that experience? What if you never needed to sleep again? What if you never needed to blink again? How about if you were 20 feet tall, or had gray skin? What if you had extra senses? Such as the ability to see infrared and ultraviolet (e.g. like night vision goggles), or to detect magnetism (already possible), or to sense electricity?
Are you still human if you have any one of those? Most people would probably say yes. But what if you had all of them? Would you say that person, or that being, is still human if they were a 20ft tall gray unblinking unsleeping man who had no pulse, who has metal and magnets inside them?
As technology advances, this may be a real ethical issue society faces, and not just a hypothetical as it is now. Diversity is basically entropy - diversity will beget diversity. You'll have more and more unique people, and that uniqueness will compound upon other unique things about them.
Let's say a person has 56 chromosomes, in contrast to our 46. On the surface they look human, maybe even on the inside they're relatively the same in form and function. Are they human? Does something like genetics have the final word on what is human? Even if they could think, feel and live pretty much the same as we do, possessing a brain pretty much the same, and their condition would never even be noticed outside of a lab? Most people might say that person is human. But now let's modify that person. Give them gray skin. Make them twice as tall. Make them increasingly alien. Give them a language no one knows. Make them a 3rd gender. They are still as smart as any of us, and feel all the same. If you conversed with them online, you wouldn't suspect anything odd at all about them. Are they still human? People would probably say no at this point - they are different genetically and in form. People would say they're an alien. But what if they didn't come from space? What if for some inexplicable reason, unknown to any party, they were just here on Earth one day? So does the true spirit of the word alien mean something so basic as coming from another planet? If it does, what if by convergent evolution a species pretty much similar to our own evolved on another planet and we encountered them? They look pretty much as humans do, and act pretty much as humans do, yet they are from another world and share no common biological ancestor. Are they aliens? Or are they human?
With all that abstractness out of the way, consider how much people modify their bodies nowadays. It is not to far-fetched to say that demand for body modification is only limited by technology. It is fair to say that some people, even if only a few, would go pretty far in body modification if science would allow them. Consider Cat Man. What if technology allowed us to give him a tail? To let him strut around on all fours with ease? To basically be a human cat? Upon completion, if you took him back a 1000 years in history, hardly anyone would think him a man, they would think him some mythological creature. But we with proper context would still consider him a human, as that is what he was at start, and he has the same brain as any of us.
We may have to come to grips with the fact that being human is not binary - that is, the thought that you are either human or not human may become antiquated. Consider gender. Many societies have a binary view of gender: male and female. But increasingly in America and other Western societies, we are being exposed to alternative views of gender identity (list on the right). Is a person with surgically made genitalia really that gender? Are they either gender, or something in-between? If a man becomes a woman, he won't have a period, uterus or ovaries. But a woman can have those organs removed, and she can stop having her period - so is she no longer a woman? Is she some genderless thing at that point? Or is the notion of gender guided by a primacy effect, i.e. what you were first matters the most? We may have to come to understand that the idea of human may be subject to that vagueness as well. And it may even come to a point where people readily shed being human to engineer themselves into something more.
Consider a non-biological example. If you upload your consciousness to a computer, are you still human? You may have a human mind, but you certainly no longer have a human body. What if you were that computer mind for thousands of years, and the majority of your existence has been as a computer? Are you still human then? If not, how does your humanness just magically decay with the passing of time? If we took an infant and uploaded their mind to a computer, long before they gained sentience, would that mind be human? It never got to experience consciousness as a human, but its origin lies in humanity nevertheless.
If your answer to the first question of uploading is no, then that basically means the idea of a human is purely biological. You are human only because you have organs, blood, genes, and so on and so forth. But that raises the question again of transitional biology - that is, you going from a human to a cat. If we are human by body only, then at what point do we stop being human, and become something else? What non-abstract line separates what makes us human versus being any different animal? There has to be one if the answer is no.
If your answer to the first question of uploading is yes, then it invites the idea that being human is concerned with the mind. The mind is what makes us human. You could be a talking head in a jar like Futurama but you're still a human. But does this mean brain-dead patients in hospitals are not human? If the only parts of their brain that worked were what are keeping them alive, such as the brain stem, while all parts associated with their personality and memory were gone, are they no longer human? If they aren't human, then what is that warm, breathing thing on that bed? What do we call that thing? Separately, the answer of "yes" also invites a different odd quandary, thanks to convergent evolution. One can imagine that if we can upload our consciousness to a computer, we probably have the capacity to create sentient computer beings too without human biological origin. What if their mind expresses itself pretty similarly to a human? Does that mean they are human, even if they never came from a human? If it is our mind that makes us human, and there is an entity that has never been in a human body and has a mind pretty much similar or the same as our own, how do we justify the uploaded consciousness as human and the AI as not human? Is it only the origins that matter? If so, that seems like a silly proposition.
What if we discovered some Cthulu-like alien out there in the universe that had an intelligent mind like ours? Their mind is pretty much the same, but their form is quite apparently different. But if you had a regular chat with them online, you couldn't tell the difference. If Cthulu and a human had their consciousness uploaded, and both hid their biological origins, their minds would both appear "human".
So either way you swing the answer, you encounter problems as you test the limits of what is human. It appears that only be technological limitations is this an issue that's far from having to be fought in the real world. Either way, it's some philosophy for you to mull over.