My ammo can usually has 300-400 rounds in it, but that covers every firearm I brought. (For Deer, Elk, and Antelope, I always have a long range primary, short range primary, long range backup, and short range backup; often with some kind of "if the mood hits me" rifle in reserve - plus a side arm, if legal.)
Any given rifle will usually have 60-80 rounds of ammunition available (various loads, so I can use a load tailored to the type of hunting).
At any given time, during a hike... You'll find a full magazine, round in the chamber, and my right front pants pocket with about 1 reload worth of ammo. Sometimes, I won't even have anything in my pocket; I have what's in the rifle, and that's it.
However, if it's a long hike, I'll take more (planning on being away from camp for 8+ hours, or a long distance from camp). Then, I'll have a backpack with general gear, and at least 20 rounds. I have never fired more than 13 shots on a big game hunt (and I'm ashamed of that one), and don't plan on ever doing so. But... I like to be prepared.
I'm a firm believer in "one shot, one kill", and I'm not a "bang away, while they're running" kind of guy. If I shoot, didn't hear a definitive hit, and the herd spooks... I don't start slinging lead like my father tried teaching me to. I let the herd go, hoping they'll calm down a little quicker.
One of these days, it'll probably come back to haunt me. But I've been on quite a few hunts where an animal is hit, but not dead, and isn't going to run unless something spooks it (but they're also now in a spot where a kill shot is difficult, or unlikely). That's where my personal approach came from. I've seen members of my hunting parties start slinging lead at otherwise stationary (or unreachable) animals, and get them spooked into running. I generally fire one shot. If something obviously needs a follow-up, I'll send it. If not, I try to close the gap, or just let them go. (I'm sure some of you remember my advocacy of head shots from other threads. The way I set my shots up; if it's not a good hit, it's a clean miss - and safe to just watch them move out.)
So... I usually take 300-400 rounds on a trip.
I usually have about 9-10 rounds on my person (exactly 21, on the rare occasion that I'm using my SKS).
And I fire an average of 6 rounds during a hunt for multiple animals, and 3 rounds during a hunt for a single animal (including a shot fired in each rifle to verify the scope has not shifted during the 3-5 hour drive to the hunting area).