One issue that has not been addressed here is the issue "passive deterrent" of states that have relatively open ownership laws. Valid or not, I remember reading statistics of crime in states that went from stricter gun laws to relatively permissive laws. The information I read strongly suggested that such a situation was a passive deterrent, presumably since those who are prone to commit crimes were more careful/selective/hesitant when gun ownership is wide and "unpredictable" in a state.
I really don't recall the sources, but I'm really curious about this aspect. As Routurner pointed out, the actual incidents of self defense gun intervention will always be statistically small, but I think that the overall passive effect has the potential to have a greater effect.
Cross-sectional (i.e. looking across several units of comparison in a single point of time) analyses prove nothing. One fairly simple example of how such an analysis can draw the wrong conclusion, if states that are high-crime also tend to enact anti-gun legislation, then a cross-sectional analysis would conclude that the legislation is what caused the higher crime rates, even if the legislation actually improved crime rates. To do the study appropriately, you would need longitudinal data (repeated measures over time), adjustment for confounders in a regression-based model (one way to conceive of this would be to say that it helps ensure you are comparing apples to apples), and ideally a "natural experiment" (a gun policy change that was enacted for reasons other than increases in gun crime).
Here's a description of the studies that have been done, including the original one which found its way uncited, a dozen years later, into a casual conversation (and who says we academics have no impact! Of course impact can be to lead people astray as well as the opposite....):
Econometric Modeling as Junk Science