Thanks guys for contributing! Keep them coming! Let me help us out a little. I am going to give you two freebies. Let's awesome everyone has a 22LR and a shotgun (i.e. 12ga etc.) of some sort. What are your other five and why?
I said 270 because as I have stated before it was my first love!
But they are hard to beat in a light weight mountain rifle. It would be my choice for sheep or anything I have to hike in to kill at ranges out to 750 yards as well as whitetail. My next choice would be my universal big bore for bears and dangerous game out to 400 yards, 375 H&H. It would be a more traditional medium weight sporter of some type. Third I would choose 300 Win Mag for elk, Moose, kudu etc., a medium weight sporter as well. Then a 338 RUM big barreled heavy varmint barreled gun for all things beyond a 1000 yards. Finally, 308, because everybody needs one, a varmint configuration of some sort for the little critters out to 500 yards or so. I might would replace that with a 6.5 of some sort but I'd have to give it some thought. I do like 6.5s.
If we were going by continent or region. Lower 48 (270, 308, 300WM), Alaska (270, 300, 338), Africa (270, 300, 375).