There's some articles out there that Harvard Professor George Church believes that there's enough DNA available from fossils to actually clone a neanderthal like suggested in the Jurassic Park movie. There is controversy as to whether Professor Church is actually looking for a female to birth the clone, but one lady asked about the idea replied, "I don’t know. I’m in support of the science if she’s willing to do it. I would not be that adventurous of a female, no.”
I honestly don't know what the big deal is all about. I have a ton of neanderthals that walk into my pharmacy every day. Some are from corporate management, others are disguised as patients looking to get narcotic prescriptions filled. There's certainly no need to clone that which walks among us already.