My Tikka T3 (chambered in 30-06) will shoot 1/2 to 3/4 MOA consistently with 150 grain Federal Powershock. The only things that aren't stock on that rifle are the scope, mounts, and bipod.
Whether or not *I* can shoot that well... that's another story.
Take it FWIW. I know that my rifle's more accurate than I am, even with factory ammo.