Speaking of "out of the box" accuracy, the last few rifles I bought have been insanely accurate (and my luck has been at an all time high - at least as far as buying rifles with great barrels with minimal imperfections).
The most impressive, and probably never seen again phenomenon was the S&W M&P15T AR15 I bought back in 2005... back then the "T" models were top of the line, with Troy MRF mid-length free floating foreends, Troy flip up BUIS, etc. I got this rifle to the bench, not expecting much better than 1.5 MOA - and my first 5 round group measured .88".. I bought fell off the bench! From there, as the barrel broke in, the groups shrank and shrank. This suprised me to much because this rifle has a lightweight M4 profile chrome lined 16" barrel! Now, since I have added a JP single stage trigger and an H2 buffer, it shoots consistent 5 round groups into .7" - .75" with my handloads, 68gr. Hornady Match or 69 gr. Matchkings.
Another was a Remington M700 SPS Varmint .308. This rifle was fairly cheap - mainly because of the stock... I wanted a 700 PSS, but didn't want to pay for one.... after some research I found that the SPS V/T had the same barreled action as the higher end models, but with a cheap, plastic SPS stock to keep cost down. Since I wanted an adjustable cheek riser, rather than shelling out the dough for a PSS, I bought the SPS Varmint, which has a 26" heavy chrome-moly barrel. It also has the X-mark pro trigger, which I didn't care for too much. Out of the box, the rifle grouped 10 shot groups right at one MOA. After break in, I got it down to about .9". Then, I cut the groups IN HALF by simply adding a stock. I added a Bell & Carlson A5 tactical stock, which has an aluminum bedding block and adjustable LOP and riser. Then the groups shrunk to .58". Then, I shelled out $$$ for a Jewell trigger, and perfected my handloads, and found a 165gr. Nosler BT load that I could group into .47". Currently, I am working on a 168gr. Barnes T-TSX load that I believe is going to group even better, already down to .4".
Right now, I am working up a load for a T/C Icon - chambered in ,260 Rem, with a medium contour fluted barrel. This rifle, wow... I'm in love. Shoots .75 MOA out of the box...