Deer- 4 rounds (the magazine of a remington 700). I figure if I can't hit one deer with 4 rounds then I have no business hunting them. It's been years since I've needed more than one. When I first got my 270 I took 4 shots a 1 buck and he never even flinched.
Upland Birds- Limits on quail and pheasant are pretty small and they are generally pretty easy to hit, so I take one box (25).
Doves- I've never been very good at shooting these speed demons. I generally keep two boxes on me, with a few more boxes in the vehicle. I shoot fewer shells since getting my over/under. That 3rd shot is generally a waste, at least for me.
Small game- Don't hunt them, but when I was a kid I would usually have a 50 round box of 22lr when out for squirrel or rabbit- mostly because they are so much easier to carry that way than loose.
Waterfowl- 6 ducks or 3 geese. A box of 25 is more than enough, assuming that they're coming to decoys. More shells may be needed for pass shooting where the shots can be significantly longer. I haven't hunted ducks in 4 years, but a box was more than enough.
Turkey- Limit 1 per day- two per season. I take 2 shells, one for each barrel of my o/u.