What is the most Accurate Hunting rifle out of the box?

I am trying to decide what Make and Model of rifle I want to buy. Looking for something under $1500 (actually hoping I can put a decent scope on it with the same $1500). Accuracy out of the box with factory ammo is one of the main things I am looking at. Of course, they all claim to have exception accuracy. So, I am looking for some input from anyone out there who has had experience with some of the different options out there. I have been looking at the Browning A-Bolts (been looking at the Hunter Eclips with BOSS, like the Monte Carlo stock, not sure about the thumb hole), Remington 700, Mossberg 4x4 (really like the looks of this one) and a Howa. I am open to other makes as well. So thanks in advance for your input.

What kind of a grouping can you get at 100 yards?

I have ordered the Mossberg 338 mag. 4x4 from gander mountain ,price was 479.00 which includes a lazer zeroed scope, for a rifle that has the capability to shoot sub MOA , I say not bad value wise.The 4x4 had an average out of five 3 shot groups of 0.72 MOA.Im sure you would have to change the scope to get those average shot groups.

If accuracy is your primary concern and you need either a .308 or a .223 then Remington 700 LTR will work for you. It's intended role is for tactical use, but the price range is under $900 and it is extremely accurate right out of the box. It has a fluted barrel that reduces weight and a light weight polimer stock. So you can carry it all day long without getting tired. The accuracy is really impressive. Remington expects them to be used by police departments in high-risk situations so they poor their attention into making sure they are as accurate and well put together as can be. I know many hunters will be turned off by the polimer stock and the term "tactical" in the name. But you asked for "The Most Accurate"..."Out of the Box" and in my opinion the Remington 700 in a .308 is it.

jack, I am mostly interested in the same as you (only deer, not so much boar). But ideally, I would like the rifle I get to be able to handle taking town an Elk as well, as I would like to be able to go elk hunting sometime but it will not be near as frequent as I will be deer hunting, and likely not enough to justify buying another rifle.

Over the years I've tried out a number of different calibers ans stock types,
and have found for my personal usage (hunting) I do alot of close to med' rrange shooting in dense/heavy scrub usually on steep slopes & changable weather. So I like the heavier 30 cal family to bash through wind, foliage etc and minimise missing. Tikka T3 (and similar styles) seems to be gaining popularity, I use a Mossberg ATR .308 or SMLE .303 for day to day work. My brother uses a Marlin 30.30 or SKS for (he hunts mostly pigs), but with more precise shooting I'll take my Parker-Hale and he'll use a swedish mauser 6.5x55.
Another one gaining followers here is .300 winchester mag', Hunters are finding them suitable for different spiecies of deer from Sika up to Elk.
Other calibers large and small not withstanding.
I wont go into optics to much except to say, I missed taking a shot at a huge red stag on sunday due to extreme close range in the rain and half dark of dawn. (Iron sights still have a place in modern hunting)