I skated and rode BMX for years and years and never did much worse than scrape my knees and elbows...
When I was really young this older kid on my block told all about how you never lock you knees or elbows when you ride, especially when falling.
I did break my leg the first time I went skiing when I was about 8 years old, I wasn't going fast enough and my POS binding didn't release...twisted my leg around and snapped it cleanly, which fortunate considering it could've messed up growth of the bone if it were a more compound type facture which extended into a growth zone.