There was a guy on another forum shooting 215 gr Bergers at 1800 yards a few months ago with a 308. With a 1:12 twist barrel no less. That isn't supposed to work, but it did.
The 308 is very versatile, especially with that twist, 125-200 gr bullets can be used. I've played around a bit with 130 gr Barnes copper bullets loaded to 3050 fps. I haven't killed anything with that combo, but from others reports it is a deadly combo out to 300ish. Later this summer I'm going to load some 200 gr Hornady ELD's for it and see what happens.
I personally think a premium 165/168 gr bullet is the most versatile choice. Lighter or heavier can be used for specific tasks, but realistically that weight will do just about anything you need a 308 to do.