It was common when I was growing up to be told not to run with scissors. It seems the adults were particularly concerned about the risk of severe injury should I fall. Is there evidence that running with scissors is dangerous? Is walking with scissors safer?
This question, much like Do children accidentally suffocate themselves with plastic bags? was covered by Ken Jennings in his book Because I said so.
In this book, the Author verifies and investigates many of these well known warnings passed down from generation to generation regarding safety.
On the entry on running with scissors the Author has this to say:
Do injuries actually result when kids run with scissors? They do! The U.S. Consumer Product Safety Commission maintains a fascinating database called the National Electronic Injury Surveillance System (NEISS), a statistical sampling of emergency room visits nationwide. NEISS estimates that 4,556 kids under ten sought medical care in 2010 for scissor-related injuries, none of which were fatal.
He goes on to point out that nineteen of these injuries since 1997 implied that "running with scissors" was at least partially the cause (and comments that those kids parents must have been devastated!).