Hmm... let's ponder this question for a minute... better yet, let's start by rephrasing it: "Should your constitutional rights be stripped away from you in the name of supposed public safety?" Now we can properly answer it - NO.
People argue that guns cause more problems than they end.
"School shootings occur because people have access to guns." Common recent examples of this claim include the VT shootings and the NIU Valentine's Day Shootings. If you stop and think about it... if students on both campuses had been legally armed, the tragedies would likely have been stopped sooner. Considering the size of the classroom involved in the NIU shooting, at least 10 students would have a gun in that room. Now let's run thru the shooting - crazy gunman walks in with a visible intent to shoot. If one of those 10 or more students pulled out their gun, it is likely that NIU would not have had as many casualties as it did. Same with VT. If students in the classrooms had been armed, they could have stopped the shooter.
"Kids accidentally kill themselves while playing with their parents guns." Here's a thought - lock your gun up. Keep out of reach of children isn't just a suggestion for perscription drugs and household cleaners. If you're worried your children will get curious about the gun, do what my grandpa did - take the kid out and let them shoot the gun in a controlled situation in which they cannot hurt anyone so they won't get struck by curiosity later and go play with guns when you aren't home.
"Shooting sprees happen because crazy people get guns. By not allowing anyone to have a gun, this prevents them from falling into the wrong hands." They have forms that people must fill out in order to get a gun. They have to pass certain tests. They have to wait a certain number of days before they are actually able to get the gun. Limitations are already placed on our Second Amendment rights... you cannot take away the right completely.
Here's something people don't always consider - if America were to make guns completely illegal, there would be an uprising of organized crime. The rusult would be similar to what happened during prohibition - mob bosses and others becoming organized with a sole goal - to make liquor (only in this case guns) available to those who wanted it and were willing to play with it. By making guns illegal, people similar to those in the days of Prohibition will rise up and create an even more dangerous society. Consider this - guns are illegal, that means police cannot have guns. If the police cannot have guns, and criminals get ahold of guns via the black market, the criminals are unstoppable. Pepper spray is not going to beat a gun. That's like putting up scissors and trying to convince everyone that they can defeat rock.
Taking away the constitutional rights of Americans gives the government even more power - something that is dangerous in and of itself. But taking away the constitutional right of the American people to bear arms... that is even more dangerous.