Well, Neandrathals were actually another species of humanoid that died off, while at some point they lived parallel with homo sapiens (same time period, occasional territorial battles?).
I'll agree with the essence of the previous posts though ... its kind of useless to clone a Neandrathal because he or she would be too human-like- it wouldn't be able to live a happy life among humanity, and it would be too humanlike for us to feel good about exploiting it for our own gains.
Prehistoric ANIMALS though ... is definitely a win for cloning. Im just kind of against the cloning of prehistoric people. Although, clones of Jesus and Hitler would be interesting. Maybe have them attend the same elementary school.
It's curious that so many people think that cloning a Neanderthal would be useless. In fact, it would be one of the greatest boons to psychology, neurology, biology, and medicine that we could ever have hoped for. Think about it. The closest primate we can compare ourselves to is a chimpanzee, whom we share a common ancestor with many millions of years ago. Neanderthals? We share a common ancestor a paltry 400,000-500,000 years ago. So basically, if we cloned a Neanderthal we would have a very closely related being with which to compare of psychology and anatomy. What we would learn in practical application would be incredible.
Neanderthals had immense resistance to bacterial infections. Why? If we had a Neanderthal to study, we could isolate the mechanisms responsible and put that remarkable information to use.
Neanderthals, as it turns out, were just as clever as we were with a brain to body mass ratio that was equal to ours. What does that mean? It means that even though they were intelligent, they have an intelligence that evolved differently than ours and may very well be of a different category than ours. Imagine the insight that would give us when it came to neuroplasticity, learning mechanisms, and neurological conditions?
So actually, I posit that cloning a neanderthal would produce an immense amount of very valuable knowledge. And in fact, I would suspect that a Neanderthal would probably fit very well into Homo sapiens sapiens infrastructure if it is surrounded by that infrastructure from birth. He/she would enjoy sitcoms, the internet, and probably Elemental: War of Magic. The question, though, is largely an ethical one. Should he/she be considered human for the sake of moral consideration? For some reason, these kinds of questions tend to make people squeemish. If it were up to me, I would create a provisional ethical system for a cloned Neanderthal that was ultimately exploitative, but gave that individual a high standard of living and comfortable conditions. In the end, I think the mountains we could learn surpasses minor infractions of liberty.