Where I grew up, there was a bagel bakery, or "bagel factory" as we called them, in every strip mall. One of them was owned by the husband of my high school English teacher, and one day in class she demonstrated to us proper bagel sliciing technique. It must have made an impression, because I remember it--and use it--to this day. What you do is to slice halfway into the bagel toward you, and then turn the bagel around to slice outward from the middle. I don't recall ever cutting myself while cutting a bagel.
According to the Wall Street Journal, I'm in the minority, and "bagel-related injuries" are a prime source of danger, with 1,979 people showing up in emergency rooms in 2008 because of improper bagel slicing technique. This obviously does not include those who cut themselves but did not require a visit to the emergency room.
There is a small industry of bagel-slicing devices intended to help you avoid bagel-related injuries. The Journal article has a whole video on them. Because I make my own bagels, I've been given many of them as gifts over the years, including the Brooklyn Bagel Slicer featured in the article. I still just prefer to slice the bagel with a knife however.
According to the article, there are more "chicken-related injuries" than any other food injuries. These are compiled by the National Electronic Injury Survey System, an arm of the U.S. Consumer Products Safety Commission. As far as I can tell, the chicken-related injuries must have been injuries from the use of some kind of tool when cooking chicken, not, say, getting a bone caught in one's throat, because the NEISS Coding Manual says not to code injuries from food.