Illegal guns go mostly to organized crime. Most "garden variety" petty thieves don't get guns like that. Large gangs can afford guns, but they tend to go against big targets, so most people don't have trouble with them.
Besides, it's not that there's no crime in Europe, too. Less gun-related suicides, sure, but criminals can be just as deadly with a knife, and organized crime is certainly equipped with guns (though an average Joe shouldn't have problems with the latter, they usually go for bigger fish). Glasgow, for instance, manages a murder rate several times higher than many US cities, despite being located in Great Britain, where getting a gun is difficult. Even in Krakow, my home city, there are places where you either need good football club connections or a machinegun to survive in at night (that said, there's hardly anything interesting besides hooligans in there). Banning knives, or any other weapon, won't help it. When the government classified baseball bats as weapons, they just switched to golf clubs. To remove violence, other measures are needed.
It's true, though, that removing guns would reduce the number of suicides and gun accidents. However, the former is again, a symptom of a much bigger problem. I believe that in every case, the root cause should be worked on, not the symptoms. Suicide prevention is a much more complex issue and removing the means doesn't ultimately solve it.
As for accidents, they're caused by human carelessness or downright stupidity. If you're gonna remove guns for that reason, you should also get rid of cars, copper wires, tall buildings, bridges, bodies of water bigger than a puddle, booze, fireworks, power tools and animals. You've got millions of responsible drivers, then you've got that dolt who downed three beers and thought he's still good for a drive... Idiots like that actually kill more people than die from bullets in many first world countries. Training, education and punishing the guilty are the only things you can do.
A senile, retired cop shooting a guy in a movie theater is a tragic accident, and he will probably be held responsible for that. It was a murder, as far as the law goes and the whole theater saw it. I can hardly see him getting treated lightly. Violating basic rules of savior vivre is no reason to kill someone.