[Glyptodon]

I can't say "most" but there are plenty of semi-automatic rifles used for hunting, at least in the US.

The legalities of what kind of rifle you're allowed to use to hunt what where and when and the particular ammo and how big of magazine can be used are somewhat arbitrary and vary from state to state and game animal to game animal. I think at least 48 at states allow some form of hunting with semiautomatic rifles.

In some parts of the country "Bubba'd" SKS guns are pretty popular for hunting deer I think. (Google image search "bubba gun sks" for a general idea of what's going on - converting a wood stock and 10-round stripper clip magazine to polymer with detachable box magazines, which is a pretty good illustration of how the same gun can look a lot different.)