I've had a times times where I blew my first shot and dropped the game with a follow-up shot. All but three of these occasions, I was using a bolt gun. On the other three occasions, I used, respectively, a single shot rifle, a .38 revolver, and a Kimber .45.
While I'm against hosing bullets at game, I strongly encourage having a follow-up shot available. It's a damn shame to have an animal that you've just shot at begin to run away before you can put it down with a follow up. That revolver follow-up shot I made was on a javelina that I had hit well but which was still standing and showed signs of getting ready to run. A second shot with the .38 put it down.
I've carried a SMLE in the field hunting with its 10-rd magazine full, and felt a little silly (never having fired even 5 shots on one occasion at game) but it was nice not having to carry spare ammo in my pack. I've offered my SKS as a spare rifle to a man who was offered an impromptu deer hunt but had no rifle with him. He seemed shocked. I explained that I had softpoint ammo for it, and that the area we were in, with fairly dense brush, would keep the shots close enough. If he only fired the number of shots necessary to put the game down, than it didn't matter how many more were below it in the magazine, did it? He declined, and chose another offered Sears brand .30-30 that our host offered. [shrug] I didn't see much difference.