I don't have kids (which is just as well, as knowing me I'd probably drop them before we'd even left the hospital
) but I fell head over heels down a set of uncarpeted wooden stairs aged 4 or 5 and hit my head on the concrete at the bottom - I screamed my head off but was absolutely fine, didn't even need a trip to hospital. I can still remember the feeling of everything spinning round me as I tumbled down!
I made a 'kite' out of paper and string and tried to fly it out of my bedroom window, by dragging a chair over so I could reach. My mum came in to find me bent over at a 90 degree angle with my top half hanging out the first floor window. The bollocking I got afterwards is one of my earliest memories 
Around the same age I wanted to get a book down from the top of my floor to ceiling bookshelf. I piled a stack of books on my desk chair and climbed onto it, overbalanced and grabbed hold of the bookshelf, which wasn't attached to the wall. It started swaying and luckily I had the sense to let go - got some massive cuts on my back, but nothing compared to what would have happened if I'd brought it down on top of me. To this day I still don't think I've confessed to my parents how I cut myself.
I ate about fifty ibuprofen, thinking they were sweets, and didn't tell anyone when I got stomach ache for days as I thought they'd be cross with me for stealing. I was so incredibly lucky it was ibuprofen and not paracetamol 
As a young teenager I also knocked a sharp knife off the counter, jumped back and watched as it embedded itself point down in the laminate floor where my foot had just been. I also used to regularly clamber out of my first floor bathroom window at night, only the top half of which opened, and perch on the sill to look at the view (still haven't told my parents about that one either - can you see a theme here..?) I'm amazed I'm still alive really 
On a more serious note, a relative of mine accidentally hanged himself when he was a teenager, and would almost certainly have died had his mum not called him and gone to check why he wasn't coming down. He was in a coma that was expected to last up to several months and his family were told he might have massive brain damage when he woke up, to the point where he might not be able to function at all. Three days later he was sitting up in bed chatting away, absolutely fine apart from needing physio and slurring words occasionally. Humans are amazingly resilient!