Interesting divergence here. Seems there are two dominant answers:
1. I hunt with a "traditional" (bolt/lever/break) action rifle that only has an internal (if any) magazine, or a detachable (but I only have one) box mag; "the hunt" is the thing, and I should be able to get the job done with a single shot ... or with one follow-up at most ...
2. I hunt with a rifle (or a knockoff) originally designed for combat/self defense, that has detachable, large-capacity magazines, of which I have many; it is adequate (some might say overkill) for hunting purposes ...
I wonder how this thread would develop if the OP's question had been worded differently? I.e., Why type of rifle/action do you prefer to hunt with?
Personally, put me in #1 above. I like to hunt with "traditional" hunting rifles, mostly bolt or lever action. I take a box of cartridges with me on the trip, and only a handfull (magazine-full) when afield each day. Only twice in all my years of deer hunting have two shots been required, both second shots being to hasten the demise of an animal that was dying anyway. (Not claiming to be a perfect shot by any means ... I have missed completely on occasion.)
I do have an EBR, though, and I have multiple magazines for it. It's just not my hunting rig. Interesting question, and interesting responses thus far.