Muzzle control is one of the most important firearm safety skills, and unfortunately, like keeping the finger off the trigger, it doesn't come naturally to people - it has to be a conscious, learned skill.
Rule # 2 of Jeff Cooper's Four Rules of Firearms Safety is, "Never let the muzzle cover anything you are not willing to destroy."
Twice I've been in a classroom of students when the instructor calls up a student to demonstrate how to shoulder a rifle. Sure enough, the student swings the gun around sweeping the muzzle across the class, and everybody ducks under their desk or table. This of course allows the instructor to go over that safety rule with that episode as a reminder - I almost wonder if the instructor knows this is going to happen, but I'll chalk it up to coincidence.
Of course, our motion picture media is also full of poor examples of following this rule:
And of course our beloved politicians during publicity shoots:
Keeping the muzzle pointed in a safe direction all the time is an absolute must. Even if you're checked the firearm and believe with all your heart and soul that the gun is unloaded, you can't have a different "unloaded" behavior than "loaded" behavior. Otherwise you end up making (Caution: Links have graphic images of "accidental" self-inflicted gunshot wounds) mistakes like these.
Another note about muzzle control that was brought up during the Hunter Safety Course my kids took last year is concrete floors. I've always focused on keeping the muzzle pointed down, but you also have to be aware of concrete or very hard floors and where a ricochet may strike. Keeping a gun pointed at the concrete floor isn't very safe if the shot ricochets and a bullet or pellets bounce up into someone's undercarriage. Keep it pointed up or in another safe direction at all times in those situations.
Be aware of your muzzle at all times, do not let it point at anything you do not wish to destroy, and even if all other safety rules go out the window, this one rule could eliminate almost all firearm-related accidents.