There are a number of posts in this thread that I agree with, and a number that I found pretty frustrating too. Here's my take on things.
If I'm out hunting, whether it's still hunting or on my way to a stand, and I come across a deer that is obviously badly wounded, I will not hesitate to shoot it, whether it is a trophy buck, a spike buck, or a doe. I would like to stress BADLY wounded, not a deer with a limp, I mean something with a leg blown off, or covered in blood. If I have time to observe the deer's injuries, I hopefully will have time to decide what to do. If I heard a shot before seeing the deer, that makes my choice easier. I will definitely shoot the deer, just to make the tracking job easier for the hunter who already shot it. In my mind, it's his deer. if it was a bad hit, I'll just swallow my tongue. I'm not willing to get into an "I saw it first, yeah but I shot it better" arguement with a guy with a loaded gun in his hands. If the deer appears to be badky hurt from a previous encounter, but I don't have the right tag, I'll still shoot it to put it out of it's misery. It might survive the winter, but it will probably die from predation shortly, all I'm doing is saving it some discomfort.
If I shoot a hurt animal even though I don't have the right tag, I will NOT report it. If I feel that I did the right thing, but know that by the letter of the law I did not, and will be punished, all that matters to me is that I did the right thing. I'm not going to make trouble for myself by calling the autorities, because even if the court does decide I did the right thing, and they probably won't, it will still cost me an arm and a leg to get that decision.
I have also "finished" animals that were hit on the road. Racoons, rabbits, and 2 deer. Both deer were hit in the summer, they were dying, so I sped them on their way, one with a shovel, and one by cutting it's throat, and left them there. I'm not driving around with a dead deer in my truck out of season.
Anyways, that's my 2 cents.
Cheers.
Tim