Modern Sporting Rifles are most often used for sporting purposes aside from hunting, mostly different forms of Target Shooting and competition. Right now there is a massive interest in 3-gun shooting sports. There are hunting uses for semi-automatic rifles for smaller game, here's one example (Because it's entertaining!):
Of course, if you shot a bear with .223, you'd likely just annoy it. A .45-70 lever action is what you need. It's not semi auto, but it's light weight enough to carry and actually capable of doing some damage.
.50BMG rifles, including the M82 are available to the public. They are quite expensive and obviously completely impractical to carry anywhere. Strangely they aren't used in crimes. I mean in the history of the US, no one has ever been murdered with a .50BMG.