After almost seven years of breath-taking adventure, we had our first broken arm this week Jeslep - not my son, but one of his pack that I regularly oversee. The best we can do is to try to get them to think safety first without making them paranoid, and prepare for those times that they don't, or someone else doesn't.
I'm the leader of a group of young kids, mostly boys, in the Scouts organization. As much as we try, there's always one kid that doesn't listen, and usually at least one monkey that sees and does. On a hike last week, one kid last week came running towards me full tilt, off trail and off-balance, through poison ivy and thick vines on the forest floor. As I yelled for him to stop, he ran down a hill and crashed into a bush. He was fine but could have tripped at any moment, not to mention losing an eye or two in that bush. Even the trail we were on was littered with obstacles.
I wasn't your typical girl as a kid. I loved doing the same thing, but I wasn't responsible for anyone else then and I was lucky - my first broken bone was when I as ten and I got it playing hockey. Girls can be just as breath-taking as boys.

Like MostlyHarmless, I stay sane by separating the minor and major stuff. I don't stress over the minor stuff. They are going act impulsively, daringly, and with that special irratic lack of coordination that only kids seem have, and they are going to hurt themselves. I try to anticipate it, deal with it, and I try to teach them to anticipate and deal with it to.
I'm teaching my core of three to be proactive about "just in case". They all carry a backpack to school every day so they also take a pack bandaids, along with extra water and snacks, a mini flashlight(they're still scared of the dark), a change of clothes and a raincoat. It's really cool when they remember to use them, and a very neat moment when they tell their friends that they should do the same.
I am very proactive about the serious stuff. There are things that you just can't compromise on. We're prepared to bug in or out at home, and my husband and I both have our emergency info with us at all times, along with a BOB. Emergencies happen so do yourself a favor and be prepared for them. It'll give you peace of mind.
It's a fine balance. You have to on guard, ready to act at any moment, and be able to live your life without constantly feeling on guard. When something happens, deal with it and then reassess so it will be smoother next time.