Stringent gun control laws can work. IMO, all handguns and automatic or semi-automtic rifles should be banned. Basic hunting rifles, and rifles used for protection in remote wilderness areas, could be permitted with strict regulation (I'll let elkman sort out the technical details). There would be a period of great difficulty, as rounding up the current massive stockpiles of guns designed specifically for person-killing would be a difficult and ugly process, but that's no reason not to do it. A significantly safer society ten years from now is worth the risk.
And, furthermore, it's entirely possible. A thriving, widely-available illegal gun market in a post-gun society is a fallacy, for several reasons.
First, economic pressures would heavily factor. Take away legality, and the value of illegal guns would skyrocket. To the average low-income criminal, an illegal gun would become a commodity far beyond their means, the first commodity sold in dire times, or the first thing stolen from them by other criminals. There have been several excellent papers published positing that gun ownership by the lower criminal class would become economically untenable within a short period of time, because the value of the gun itself would cause them to be reported, sold, or stolen and sold, and filter them upward out of the poorer classes. The government could dominate the illegal gun market through bounties, at least among the lower classes (the group most likely to use guns in random violent criminal activities). Economic realities would make the boogeyman of armed crackheads preying on an unarmed population untenable. It would be like a street thug running you down with a Bentley.
The reason that illegal guns would have such a high value is because they would, in fact, be rare. Illegal guns would be light-years easier to regulate and interdict than, say, illegal drugs. Guns are heavy, bulky, complex machines made of metal, meaning their creation, transport, and hiding would be difficult tasks. To make an illegal gun requires expertise, raw materials, production capacity, and mechanization--a serious manufacturing ability at your disposal. This would be next to impossible to pull off domestically. I see little difficulty in the ATF being able to prevent the wholesale production of firearms within our borders, giving the space and materials necessary, and the mechanical complexity involved in making a gun. This isn't growing weed in your backyard, it's building a machine from scratch. Melting and reshaping metal. Forming small, specific parts. Good luck with that in your woodshed.
That means new illegal guns would need to be imported, but that would be very, very difficult to accomplish profitably. Unlike drugs, guns are metal, and therefore much, much more easily detected by border guards and simple electronic barriers. Guns are also bulky and heavy by comparison -- you can't move guns in any quantity without serious shipping capacity-- trucks, planes, etc. That make shipments easier to detect. Given the space, complexity, and difficulty manufacturing guns, the profits margins can't compare to the 100K worth of cocaine you can grow in a jungle using unskilled labor, pack onto a donkey, and walk across the border. Running guns into the US would be an extremely difficulty, perhaps impossible process to pull off in a percentage that would make the business worth it. The costs would be astronomical. Every gun made would be the result of intense effort and labor, meaning each lost shipment would actually hurt. Basically, the exact opposite of the drug war. We have the technological law enforcement resources to win this one easily. Would there be a market for wealthy consumers? Sure, just like anything else. But those buyers aren't the main problem anyway.
Give it a few years and the domestic stockpiles would disappear under floorboards, or be rounded up, quicker than you think. If mere possession of a gun was a crime, it'd be a rare event that they were carried around, or actually used in criminal endeavors. And such possession would be an excellent predicate offense to take criminals off the street. Further, gun crimes would obvious carry much weightier penalties, discouraging their use. Suddenly, to keep your gun and stay out of jail, you could never use it. That result works just fine.
Also, ammunition would run out. Guns require bullets, and bullets are manufacture goods. That means there are two points of interdiction, which is very helpful in combating gun use.
Finally, guns are machines. Machines, at some point, break down. I understand that guns, thoughtfully maintained, can last decades, but that's with the support of total legality. Twenty years out, many weapons would begin to lose functionality. People would begin to forget proper gun maintenance methods and techniques. And anyone stashing guns for decades isn't the problem to begin with. Gun culture would have less hold.
We can get there. Other nations have shown that it's a better way to live.