I've used one of my guns several times in the last few days to dispatch a couple of rats who had invaded one of my buildings.  This was just my 22 cal rifle and I used shot-shells which work like a charm on rats.  It is nearly impossible to kill more than one rat by any other means that I've found.  They are smart creatures who quickly learn any kind of trap or poison.

One of the most common needs for a firearm is to put large animals out of their misery.  Fairly recently a local donkey got into trouble.  In that case we did have a vet come out and she killed the animal with an injection, but it cost $700 and she was able to come out fairly quickly.  I would have just shot the animal rather than have it suffer and slowly die over 48 hours.  And if I'd known that the creature would have to be put down, I'd have spent $1 on a shell rather than $700 on a visit from the vet.  I would _not_ have taped a knife to a stick and tried to stab the creature to death or whatever 'option' you urban morons might dream up.  Had I not the option of instantly killing it with a shot to the brain, the creature would have died a painful death over the course of a few days.

It is pretty common to see an animal who was hit by a car and is suffering in pain beside the road.  I've seen it on average of probably once per year.  A responsible person will put the animal out of it's misery.  I don't live in a 'rich' area where there is a lot of 'services' who will come out and deal with the problem (e.g., sheriff, animal control, etc.)  The resources just are not there.  I've not had to kill an injured animal on the roadside mostly because so many people carry guns in their cars in my area that someone else has always come along before I needed to perform this duty.  Thankfully.  I would not like to have to perform this duty, but I would rather do it than to think of an animal suffering for as long as it takes to die naturally, especially since scavenger animals usually start in before the animal is totally dead.