Whilst it's one of those things that the weird kid at school always claimed to have mastered (but, of course, it was against his training to show you), the Vulcan nerve pinch appears to sit well within the "fiction" part of science fiction.
The theory is that the pinch blocks the passage of blood and nerve signals, presumably specifically in the subclavian artery and vagus nerve which lie pretty much smack in the targeted area. In fairness, there are some theories to suggest that trauma to the vagus nerve (when you get hit in the balls, for example), could lead to unconsciousness, but it's pretty tenuous. Alternatively, it could be eliciting the baroreceptor reflex, causing a drastic drop in blood pressure.
In practice, however, it just doesn't appear to be possible. The "real life" equivalent to the Death Pinch is the Dim Mak - a mythical move in martial arts that supposedly kills or incapacitates your opponent with one touch - but it is based on the ancient idea of meridians and there is little scientific evidence to suggest it exists. You can, of course, render someone unconscious or even dead by applying pressure to the neck area and cutting off oxygen to the brain, but this can take many minutes.
So near, yet so far.