Kyle Munkittrick of the "Science Not Fiction" blog argues, "Yes, we should clone Neanderthals."
A full response to this clearly deserves more thought than I can give right now. I'm going to keep pointing to arguments about the cloning issue, as I have done in the past with respect to human cloning.
I'm completely in favor of cloning Neandertal tissue cultures. I really think we can learn a lot about our biology by understanding that part of our evolutionary history at a cellular level, and that knowledge may well help people.
But making a whole person is different. Not only in an ethical sense but also a practical one, as our ability to understand the brain and immune system in living people isn't mature enough to make meaningful predictions about the small genetic differences between Neandertals and living people.
Of course today this is all just idle talk. Someone who's talking about other extinct species, I don't take very seriously. We're talking about an ancient population of humans here. Not like quaggas; more like Tasmanians -- a group of people whose culture hasn't survived, and yet still has many living descendants. This shouldn't be a conversation about cloning, it should be about the logical consequence: adoption. Who will step up to adopt a Neandertal child, and why aren't they helping living children instead?