The attempted assassination of Rep. Gabrielle Giffords and the murder of several bystanders including a federal judge and a 9 year old girl have raised reasonable questions about the role that Arizona's relatively permissive gun laws played in this crime and in rates of violent crime in general. This is a vexing question since state-level variance in gun-related crimes is no-doubt tied up with cross-sectional variance in cultural, economic, and demographic factors as well as public policy choices, all of which are temporally related to one another and to changes in national patterns of crime and policy. Taking any slice of data and trying to sort out the various causal mechanisms at work in the face of terrible problems of measurement, endogeneity, serial correlation, and cross-level effects pushes the limits of meaningful statistical analysis.
Having said all that, economist Steve Levitt's analysis of the causes of declining rates of violent crime through the late 1990s offers one of the most convincing---in my mind, anyway---claims about the relationship between gun laws and gun crimes: there is little evidence that restricting or increasing access to guns has any significant impact on gun crimes. On the one hand, Levitt writes, "There is, however, little or no evidence that changes in gun control laws in the 1990s can account for falling crime." Making guns marginally harder to obtain through legitimate channels has little effect on criminals' ability to obtain weapons through illegitimate means including theft and purchase on the black market. On the other, "Ultimately, there appears to be little basis for believing that concealed weapons laws have had an appreciable impact on crime." Making it legal for a small number of citizens inclined to carry weapons for legitimate purposes does not significantly influence an overall deterrent against violent crime. Gun laws---in the range historically enacted in the United States---are unlikely to have any appreciable effect on overall crime rates or to prevent any determined individual with criminal intentions from carrying them out.
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