Very real.
I had the pleasure to work with the scout sniper school. On the range, they routinely make these kinds of shots out to 1000 yards with a 308. They can reach even farther with a 50 cal. I didn't get to play with them in the field but if you hang out with them, you hear about some miraculous shots.
Before desert storm, they desimated the Iraqi front line soldiers. They liked to maximize psychological effect. They would pick a target and wait hours until he was in the middle of a discussion with someone else, then they would make his head disappear leaving the other guy talking to a corpse.
Eventually the Iraqis moved back a mile from the front line, beyond the reach of the 308. That's when the Barret rifle arrived. The snipers say that the Iraqis never figured out that they were getting shot purposefully at that range allowing them free hunting until the war started.
I've heard that more and more snipers are going with the .300 win mag short, at least vs. the .308.