There is alot of talk about leather soled boots, but im a firm believer that no one pair of boots can stop you from poor riding, it shouldn't matter the boots you simply shouldn't have your feet so jammed into the stirupps that they get stuck. Also having a proper seat will save your life, I have ridden probably 60 horses of all breeds in my short life calm, crazy, and broncho status, and I swear my best tool was having a good seat and patience, so far I have only been thrown once..knock on wood.
Anyways riding safe in my experience really has to do with rider awareness. For example many people trail ride while with friends to be safe, I do it all the time. But the fact remains many of us get to talking and don't always pay attention to what is in front of us! Big no no! A lot of accidents happen this way.
Also getting complacent while riding can be a huge issue! I'm guilty of this too, for example I was sitting on one of our really quiet lesson horses one day, bareback, and with really loose reins...i spooked her accidentally with a water bottle crinkle noise...i was on the ground ten seconds later. We need to be constantly training ourselves and our horses to handle these situations. I'm not saying be paranoid, but be prepared to respond.
Lastly, if your getting on a "yeehaw horse" have someone there or at least a phone. At the rescue I worked at for five years, the younger girls (me), were recruited to jump on the new horses (those who were healthy) to see what they could do. Sometimes they were old barrel horses who took off, others were jumpers, some fresh off the track, and once a peruvian paso whom I accidentally got to rear on command (he reared vertically). Lesson here you never quite know what you could get no matter how good the rider.