The first time I watched an animal die, it was a bird we found in our front yard that had apparently been attacked by a stray cat. We placed it in a shoebox with some towels to help it relax and recover but it didn't make it, and passed away as I was watching over it. It still haunts me to this day, since I watched it happen so slowly and gradually and couldn't do anything to stop it.
On a more gruesome note, I saw a motorcycle run over a small dog and literally pop it like a water balloon. Sorry about being so graphic, but there was no other way to describe it, there was nothing left of the dog. It was a total freak accident, not really anyone's fault - the dog was on a leash and the owner was walking them far enough away from the street. It got excited when it saw the motorcycle and broke loose and darted out in front of it at the last second.