Disclaimer: I shoot benchrest
If you're looking for an OUT OF THE BOX accurate rifle, one of the varmint guns from Savage will likely be the best choice.
If you're looking for the utmost accuracy, a Remington comes in second to the custom actions, but can be reworked to approach their accuracy. It is easier to find "benchrest-quality" gunsmiths to work on Remingtons.
Accurate rifles I own:
1 Stolle Panda (6PPC, .22 PPC and 6BR barrels)
3 Savages (12BVSS-S in .22-250, replaced the trigger, shoots in the mid-threes, 110FP in .308, in a Choate stock, shoots about .5-.6, and a 110 that currently has its .243 skinny barrel (0.7-0.8 with 55 gr. Noslers at 3,900 fps) off and is waiting to be sent back down to Paul Dorsey for a nice big heavy honker in 6BR...)