It is theoretically possible – although I’m not an expert in this area. We have cloned mammals before, and so we could use the same techniques with humans – taking a humans DNA and placing it in a human egg, which can then be placed in a woman’s womb to grow in the usual way, arriving as a baby clone 9 months later.
However, this would be a huge step ethically. Scientists have to think lots about ethics when doing jobs involving human lives. Is it right to do this? Is it fair? Might it cause harm or damage? How will it effect the lives of the person being cloned, and the clone itself? And ultimately – why should the experiment be done, what can be gained from it?
So, although it might be fascinating, it is not a route we have yet gone down for ethical reasons. Will we do it one day? My honest thought is that one day curiosity will get the better of us and we probably will, but not for a while.
However, as Aaron has said, the bigger question is whether it’s ethical. To quote from Jurassic Park:
“Your scientists were so preoccupied with whether they could, they didn’t stop to think if they should.”
We have used genes from humans and placed them inside bacteria before now, to produce insulin for diabetics – this is clearly a form of genetic manipulation that is ethical (nobody is harmed to do this, and it helps a lot of people). But what would be the benefit of cloning a person?
There have been a few sci-fi films that look at this question, most notably “The Island” – if you haven’t seen it, I recommend you watch it!