I think there is a useful distinction to be made between two kinds of unintentional discharges. I think "negligent" and "accidental" are the wrong words, but I'm not sure what to call them. Perhaps "forgivable sins" and "unforgivable sins"? Let's try that.
"Forgivable sins" are the ones where your NES buddies will say that "it can happen to the best of us—glad you're ok." Putting your finger on the trigger when you're not supposed to is in that category. Even very well-trained people do it frequently when they're under stress. And I know that I can do it too: I was once caught by an instructor with my finger inside the trigger guard while reloading. I was shameful as a scolded puppy and promised myself to be more careful, but I know that it can happen again. Failing to check that the gun is unloaded is another such "forgivable sin." It helps to be careful and pay attention. It helps to work it into your routine. But good people still forget sometimes. Failure of well-maintained guns, though rare, also falls in to this category.
"Unforgivable sins" are the ones where NESers say that "he was a moron and deserved to die—and he was probably a cop." The typical example is the guy who points his gun at his friend or dog to dry fire. Once you have identified a few safe directions in your house, you know to only point the gun there when you dry fire. Pointing it somewhere else is not an honest mistake that just happens. If you point it somewhere else, you're not just forgetting a step in your routine: you are doing something you have never done before and promised yourself never to do. You have to willfully ignore the safety rule you set for yourself.
The trick, of course, is to organize your gun handling so that a sin of the first type always has to be combined with a sin of the second kind in order for someone to get hurt. Being really strict about safe direction goes a long way. Insist on a safe backstop when loading and unloading, even though you're trying really hard to keep your finger off the trigger. Insist on a safe backstop when you dry fire, even though you're trying really hard to remember to check that the gun is unloaded, and even though it is fun to wander around the house and shoot all the light switches and mirrors.
One situation that I don't have a good solution for is holstering. Some NDs happen when the trigger gets caugh in clothing, folded in holster material, or a finger while holstering. Sure, you can try to be careful to keep clothing out of the way, inspect your holster, move your leg the other way, and so on, but these are all things that it's possible to screw up without being a moron that deserves to die. Always removing the holster before holstering isn't practical when practicing. (But if you can leave the gun loaded holstered on days you are not practicing, you reduce the exposure. If the gun stays holstered from the safe to the belt and back, not much can go wrong.)