Obviously, the primary and most common concern is that the kids might somehow get hold of it. It’s a legitimate worry - about 600-800 child accidental shootings happen each year, killing around 175 kids. Precious lives lost all because the kids got hold of a gun and started playing with it.
Often times, the kids know better than to be playing with a gun, but their curiosity gets the better of them. They also probably know not to make a mess, but how many times has that happened? Other times, they discover the weapon and aren't sure if it’s real. They explore it to find out or assume it is a toy, (C'mon, who leaves real guns lying around?), and an accidental shooting occurs in the process. Careless gun owners pose a significant danger to children - not just their own, but others as well. Nearly every other day in America, a child is accidentally shot and killed...a life-death risk on the order of around 600 times the threat that registered sex-offenders pose. (NGC, 10-5-09) In other words, a gun owner is far, far more dangerous to your child than those sex-offenders people work so hard at keeping out of their community. You might also consider this: If you purchase a gun, YOU are far more likely to end up killing your child than are any of the registered sex-offenders nearby.
The catch 22 is that if you're keeping a gun for protection, then in order for it to work for protection it needs to be easily accessible. That means putting your kids at risk, (a higher risk than what is posed by community predators) in which case you won't need to worry about any criminals, because you're far more of a dangerous person to them than they are. Or you must keep the kids safe, which means locking both the gun and its ammunition safely away, which mean that it won't be readily accessible. And don't forget - bullets can be just as dangerous without a gun. As a child, a friend of mine shot himself through the hand while holding a bullet he had found on the street up to a candle to look at it. The same can happen while holding a cartridge up to a light or other heated surface, or if the firing strike is banged against something hard.