I don't have one of those stories where I was inches away from death. However, I do have instances where if one thing was different, I could have died. When I was five, I almost got hit by a car after dashing out in the street without looking to get a ball. Luckily, the car stopped a couple feet from me. Near death? Nah. Near death if the person wasn't as good of a driver as he/she was? Very possible.
The closest thing I have to a real near death situation was when I was eleven. My cat bit my ankle and it got severely infected. It was during my birthday party/sleepover, so I ignored it for an hour. When I finally told my mom, she patched it up and said that my cat got me good. As the night progressed, I attempted to enjoy my party, but my ankle was becoming extremely painful. Before I even went to bed, I couldn't walk well. Being the usually overdramatic child that I was, my parents and friends didn't believe that I was in intense pain and told me that I was fine. But when my ankle started oozing nasty puss and my leg started swelling up to my knee the next day (a Saturday), my step father intervened. He said that I needed to go to the hospital (instead of going to the doctor when the weekend was over like I was going to). Ughhh, that was a wretched experience. X-rays, them squeezing the puss out of me, and needles bending while they were in my body made the whole three day stay horrible. They told my family that if I had waited until Monday, the infection could have moved to my heart and killed me. If my cat had pierced the bone, I could have had an amputation. Close to death? Nahh, I don't think so. But it was the closest to death that I have ever been. tl;dr