I well remember these discussions from 10+ years ago, and at that time there was no serious evidence of human-Neanderthal interbreeding.
Today there is evidence from multiple sources showing some small interbreeding.
SunkenCiv has posted some of the evidence on FR many times.
varmintman: "Think really hard: What do you think the chances are that this same group of people who hated hominids badly enough to extirpate them from the planet root and branch, would have tolerated any human/hominids (i.e. human/glorified ape) cross-breeds amongst their own population??"
I'd put it to you a little differently.
Suppose you are a scrawny little ancient human just "off the boat" from Africa, 40,000 years ago, trying to migrate into Europe, and making no headway -- zero, zip, nada -- against those powerful brute Neanderthals.
So, pal, whatchagonnado?
How you going to get along with these big brutes?
What do you have to offer that they might want?
Remember, 40,000 years ago, you're no smarter than they are -- your weapons and tools are no more "high tech" than theirs are.
So what do you have that they might want?
Well, one thing's for sure, your women are a heck of a lot prettier than theirs, and if you have little ones running around your camp which look a lot like their little ones, they might see you less as supper, and more as a hot date in the big city.
Think about it... ;-)
I don't waste time thinking about idiotic stuff.