No offense overkill, please, but this is serious question.
Been reading the article in Mr. goneballistic's reply to an earlier post of mine. I have read a number of posts here on long range accuracy, but none have really addressed some issues I think important. One of my earlier posts talked of guys shooting rock 2 mi away, but they only did early morning, calm air, no expectation of first round hit, or even 2nd.

Assume:
perfectly consistent ammo
a rifle that is totally consistent
perfect knowledge of wind velocity(that includes direction if ya forgot your high school physics) at your position
So, what the hell is this idiot talking about? Well, I am curious about wind, I can stand outside and it is awfully rare for it to be in any way consistent over even a few sec time frame. Considering how the wind imparts such an effect on the trajectory, it seems like the claims in that article, and by many I hear of on these forums, and of course in movies (I love the scene in �Valdez is Coming� with Burt Lancaster where the target gets hit many seconds before the sound gets there, but realistic, with iron sites, from that elevation?, but still fun) be a bit optimistic, even for a trained military sniper.

So, can you sometimes assume the wind will average out over such distances? The 1000 yard ranges, forget the 2 miles, but I want to go try that, that is for sure.
rob the guy who be too curious about stuff

Consider that there have been a number of "one shot kills" made at ranges in excess of 2000yd, on targets that can and do shoot back. I believe the current record is held by a Canadian at 2450 Meters (1 1/2 miles) in the Afganistan mountains.
Back in WW2, German class A snipers (if faulty memory serves) could guarentee a head shot at 800M and a torso kill at 1KM, class B snipers did heads at 500 and torso at 800.
So, to answer your question, Yes a trained shooter can make first round hits at very long ranges.
It's a rare talent however, just like a top F1 race car driver is a rare talent.

As far as I know, the current "record" on an elk kill is over 2800 yards. Yeah, trained shooters, with the best equipment can kill them a long ways. I wouldn't call it hunting, but that is not what you asked.

Check out http://www.longrangehunting.com./

I'm happy to keep them on a pie plate at 300 yards from a good rest. Someday I hope to do it at 600 then who knows...maybe 1200 (hey, I can dream!).