The risk of physical danger depends mostly on where you're doing the majority of your performing. If you're mainly a stage actor, about the worst that can happen is you run into a set piece in the wings or get so into character that you accidentally walk clear off the edge of the proscenium.
More physical danger exists in the world of film, where the physical demands can be more strenuous, especially if you're pulling a Tom Cruise and doing all of your own stunts. Even if you have your own stunt-person, some scenes will be more dangerous than others.
Filming an office romance scene only runs the chance of bruising your ego (you sloppy kisser), while an on-location shot of you, waist-deep in a rice patty, somewhere in the jungles of Vietnam could end up bruising things you didn't even realize you had.
Generally, your day-to-day's most dangerous time is the journey from sofa to audition room (do I have to get up?), but there's always that itty bitty chance that you'll be a part of a horrible on-screen, real-life accident. After all, the whole reason there's a written protocol for dealing with prop guns is because even the fake ones, when mishandled, can kill you.
So listen to the assistant director/prop master/whoever is telling you to move; during a massive controlled explosion is not the best time to go full diva over how much camera time you're getting.