I spent part of my holiday going back over the (relatively) new 2016 FBI crime numbers for a few minutes. There is one data set that I've been following for several years now — the number of gun homicides in each of the 50 states. It continues to confound most people's assumptions about guns and gun crime.
I looked a few years ago at the absence of a correlation between gun ownership and gun crime in 2014. As surprising as it might sound, neither higher gun ownership rates in a state nor varied attitudes toward gun policy seem to correspond with more gun murders (or even with more gun robberies). This was still true in 2015 and now in 2016 as well. In the graph that follows, each dot is a state, plotted for gun homicide rate and gun ownership rate in 2016. The correlation here is too small to be statistically significant.

Then again, gun ownership survey data are not necessarily known for being reliable or up-to-date. If we don't want to lean too heavily on the data from Injury Prevention magazine (which I chose because it had been used by others to make various arguments), we can still get a ballpark confirmation of this concept by looking just at how the states rank.
On the chart below, you'll notice a number of states with little in common in terms of gun policy are neighbors when it comes to gun murder rates. (Note also that Florida and Alabama are omitted from all of these charts — those two states seem to flout FBI reporting perennially.)

Here's an example of what I mean: It really says something that in 2015, Texas, where any sane non-felon can attend church on Sunday with a rifle strapped to his body and then carry it across the street into his local Starbucks without a permit (please don't do this), had a nearly identical gun homicide rate as California, where such behavior would get you arrested instantly and perhaps sent to Gitmo or worse. Similar pairings of disparate states can be found between restrictive Maryland and permissive Georgia, restrictive Massachusetts and permissive Utah, and others.
In 2016, the numbers varied a bit, but the story was similar. States with extremely permissive gun laws like Idaho, North Dakota, and Vermont shared similar low rates of gun murder with very restrictive states like Massachusetts and Rhode Island. At the other end of the chart, restrictive Illinois and permissive South Carolina; restrictive Maryland and permissive Tennessee shared similar and disturbingly high rates of gun homicide. New Jersey, where out-of-state drivers are sometimes arrested for having their guns anywhere in their own cars, is roughly comparable to Wisconsin, a permissive concealed-carry state where you can carry your gun on the city bus and no one can tell you otherwise.

Beyond just the idea that criminals don't follow gun control laws, the main problem is that the law is rarely a good preventative. Gun laws are primarily used after the fact to pile up longer sentences upon known (or suspected) criminals who get caught with guns. They are rarely used in a way that prevents mass shootings or common gun crime. Even when it comes to illegal purchases — one area of the law that should serve as a clear preventative — the federal government has been famously loath to prosecute known violators.
One thing that actually does correlate with higher gun ownership is a higher gun suicide rate. It would be interesting to have a debate over gun control that centers on suicide, but we never do that. And unfortunately, a lot of statistics are tossed around carelessly about "gun deaths" that deliberately try to conflate gun crime and gun suicide in the cause of making the case for gun control seem stronger than it really is.
Even if the "more guns, less crime" hypothesis vastly overstates the case, there's no evidence that a more permissive legal regimen invites more gun crime, or that any peculiar set of gun laws represents an ideal for minimizing crime. If you want to figure out why Maryland has so many more shootings per capita than Texas, or Alaska than Massachusetts, you're going to have to look at other differences that take you beyond a myopic focus on gun policy.