I don’t know how well a single case-study can be generalised, or applied in a different cultural setting. But since jozzas’ answer on the Australian gun control act exclusively relies on a paper that completely misrepresents the evidence here’s another stab at it:
In 1996, after a mass shooting with an illegally purchased but legally available semi-automatic weapon in Port Arthur, Tasmania that killed 35 people and wounded 23, Australia enacted the National Firearms Agreement (NFA), a strict ban on semi-automatic weapons and stricter requirements for acquiring a weapon permit. They also enacted a compulsory gun buyback scheme taking effect immediately which resulted in 600,000 guns being bought back from the state, at a cost of 500 million AUS$. The government levied a 1% addition in income tax for one year to finance this.
Data & evidence
The following gives a broad overview over a huge mass of data. I tried my hardest to represent the data fairly; however, by necessity I leave out quite a lot (otherwise I’d have to publish a paper). Most of the missing data and justifications can be found in Leigh & Neill  which gives a truly excellent run-down of the evidence, along with a careful explanation and justification of the statistical methods used, and a comprehensive explanation of the limitations of the data. In fact, this latter point makes the paper stand out particularly.
Massacres. In the 18 years prior to the enactment of the NFA, there had been 13 massacres in Australia involving guns (defined as killing ≥ 4 people). In the years since, there have been none. However, while such large-scale killings are obviously tragic events they contribute relatively little to the overall rates of deaths by guns.
Murder rate. Australia has generally had low levels of violent crime even before the ban. Furthermore, there’s been a steady decline in the number of firearm-related deaths since the early 1980s [1, 2], in particular, there was a 47% decrease between 1991 and 2000. This was accompanied by a similar decrease in non-firearm related murders.
On the other hand, there was a clear acceleration of the reduction after the NFA was enacted, but  found that this reduction falls short of statistical significance.
Suicide rate. What they managed to show, though, was that the NFA buyback contributed strongly and significantly to a reduction in suicides. To ensure that they weren’t just looking at a reduction over time which started before the NFA, they compared across states and correlated reduction with number of guns bought back by the state, and find that more gun buyback by the state results in more reduction in suicide with a statistically significant trend (R2 = 0.7685, p-value = 0.004% – this is a very robust statistic that cannot be explained away by any other factors that the authors examined). The gun buyback led to a reduction by 1.9 per 100,000 for each 3.500 withdrawn guns per 100.000 individuals (95% CI), which is a 74% reduction.
This state-dependent trend and its correlation is shown here:
Compensation. Both murder and suicide rates declined globally, that is, reductions in gun death weren’t increased by use of other weapons. However, in the first few years after the NFA, non-gun suicides were briefly raised, continuing a prior trend, before dropping as well. No such trend exists for homicides.
Cost. The gun buyback cost 500 million AUS$. On the other hand,  estimates that the 200 annual deaths thus prevented correspond to an economic saving of 500 million AUS$ per year. This would correspond to a 7 billion AUS$ cost saving.
Could this money have spent differently to get a similar (or better) reduction in gun-related deaths? I couldn’t find any data analysing this. However, the buyback was essentially a one-off cost so amortised over time no ongoing intervention could have a better cost-benefit relation.
As mentioned, the robust data analysis shows a marked reduction in suicide rates.  goes into more detail to improve the robustness of the analysis by doing subsampling and trying (unsuccessfully) to explain the reduction with other variables.
Lee & Suardi  have argued that no such reduction exists for homicide rates because the time series data doesn’t show a “structural break”. That may be so ( didn’t find a statistically significant reduction for homicide rates either). However,  notes that such structural breaks cannot be assumed to exist due to the large number of factors influencing death rates.
Baker & McPhedran  claim that even the suicide rate reduction is not related to the NFA buyback. However,  notes that this paper is deeply flawed since it wouldn’t infer significance even if homicide rates had been negative in the years after 2004, and that the authors of  “should know better”.
Overall, the NFA and buyback were correlated with a significant reduction in firearms related deaths, and no balancing increase in non-firearms related deaths.
Putting things into perspective
Is this evidence convincing? Yes: It is the best evidence we have, and while statistically flawed methods find no effect, correcting statistical mistakes invariably finds a significant reduction. And in fact, it is the best evidence we could hope for, because it is the kind of signal we would expect to get if we knew that there were a real effect: no sharp break but a steady decline. In fact, in the words of the authors of ,
from the perspective of 1996, it would have been difficult to imagine more compelling future evidence of a beneficial effect of the law.
-  Jenny Mouzos & Catherine Rushforth, “Firearm related deaths in Australia, 1991–2001”, Trends and issues in crime and criminal justice, no. 269, Nov 2003
-  Andrew Leigh & Christine Neill, “Do Gun Buybacks Save Lives? Evidence from Panel Data”, American Law and Economics Review, Vol 12 (2) pp 462–508, Aug 2010 [PDF]
-  Wang-Sheng Lee & Sandy Suardi, “The Australian Firearms Buyback and Its Effect on Gun Deaths”, Contemporary Economic Policy, Vol 28 (1) pp 65–79, Jan 2010 [PDF]
-  Jeanine Baker & Samara McPhedran, “Gun Law and Sudden Death – Did the Australian Firearms Legislation of 1995 Make a Difference?”, British Journal of Criminology, Vol 47 (3), 2007 [PDF]