For a game rifle, 3-9X or 4-12X is fine, easy enough to get a good shot on a game animal at any range I am comfortable to take a shot.
My Varmint-LR Rig has a 6.5-20. I have another Varmint rifle that has a fixed 36X Leupold benchrest scope, which frankly was a mistake. It is quite difficult to find targets because of the narrow field of view, and the eye relief is ridiculously critical. If you head/eye is not in the perfect spot (± ~1mm) you can't see a damn thing.
I never understood the attitude some people have that "This is the way the military does it, so this is the way you should do it". The Military has specific reasons why they do what they do how they do it, and generally speaking, for your average hunter/shooter those reasons probably do not apply. If you want a fixed power scope for a military Sniper rifle, 10X is a great choice, for the reasons stated. Police are probably fine with lower power, because the engagement ranges are shorter (I remember haring conflicting numbers for this, some claim the average shot is 70 yards, but I have also heard it is as low as 50 yards)
I am not a sniper, and I am not limited to a fixed power scope, A good variable gives you lots of magnification when you need it, and less when you don't.