A group of scientists is going to try to map the DNA of Neanderthals.
http://www.newscientist.com/channel/being-human/mg19225772.000-blueprint-for-a-neanderthal.html
I imagine when they are finished, they will find that we are extremely closely related, but we shared the last common ancestor about 200,000 years ago.
Neanderthals were pretty cool. But so was Homo Erectus and Archaic Homo Sapien sub-types.
Well, the first results from the Neanderthal DNA study are already in.
Looks like there are sufficient differences that the common ancestor was about 600,000 years ago. This would mean that Neanderthals are more distant cousins that we thought.
http://www.newscientist.com/article/dn10581-neanderthals-have-genome-chunk-sequenced.html