Well I live in the UK and one thing I can tell you is this, we have one of the lowest levels of GUN crime in the world because it is so very hard to get a gun licence. Because of this there are less guns available in the country overall so less criminals have the chance to get them.
But that wasn't the question. There are still violent crimes, with and without guns. The availability of guns doesnt really effect the overall crime rates, just the ones that involve guns.
So no, gun regulations don't stop crime happening, but they do lower the rates of gun related crimes. For example, the amount of gun related crime in New York City in a week is roughly the same as in the whole of the UK in a month, possibley a little more. Actual crime statistics though are a lot closer.