I've got the 308 win and have had mine for about 2 years now. I haven't shot it further than 400 yards, and have always been curious to see how far out this thing can touch effectively. I've done google searches to no luck and am wondering if you guys would happen to know.
The response to your question would hinge entirely on what you mean by the word "touch". The .308Win has been used to compete at 1,000 yard matches since it first arrived on the scene, back in 1952. In fact, it set a few records, during that time. With the right bullet selection, it can be relied upon to touch paper targets at that range, and more, really.
Now, if by "touch", you mean kill a deer, or other thin-skinned medium game, then the range falls to somewhere around 400 yards, and then only with a good deal of practice, at that range. One of the best bullet weights for the amount of case capacity the .308 offers, is the 150gr offerings by various makers. Factory loads push these bullets to around 2800fps and the hand loader can duplicate, and even slightly improve upon, that velocity. In practical terms, this particular loading would have an effective range, without holding above where you want to hit, of about 275-300 yards. For most riflemen, that is plenty far and again, those distances should only be attempted after you've practiced quite a bit.