Denmark is quite odd.
If you own land, live in the country or hunt, you can own a hunting rifle - but it requires a permit that has to be renewed every year (and costs money). Shotguns are okay, but I imgine most cities have ordinances against them, so mostly farmers own them.
Pistols or regular rifles for private citizens - forget about it. The ONLY way for a private citizen to own a pistol is to be an active member of a sports shooting club. Even then, you cannot apply for a permit, but your clab can petition the police for you to get one. Once you get a permit, you have to continue to be an active member of the club (i.e. shooting regularly). If you stop going to the club, they are required to call the police - your license will be revoked and you will be required to turn your guns into the police (until you get a new license or you sell them). In addition, when I lived there, only 365 permit were issued in the country for 9mm handguns. If all the permits were already out, you could not get another one until someone lost a permit. In addition, handguns had to be disassembled and stored in two separate places under lock and key.
ON THE OTHER HAND - the Danish "Home Guard" (like the US National Guard) keep all of their weapons and ammuntion AT HOME. When I lived in Denmark, every member of the home guard had either a H&K G3 w. 200 rounds of ammunition, or an MG-42/59 w. 600 rounds - or other stuff like the submachinegun. I'm not sure the 84mm Carl Gustavs got to go home with people, but you get the point. Home Guard units are local, so they can organize and be ready to fight in about an hour after an alert. In addition, all officers in the military were required to keep their service pistols (SIG 210) at home with ammunition.
So it's an odd dynamic - in that there are LOTS of assault rifles and machine guns in peoples' homes in Denmark, but very strict guns laws for citizens. I don't think private ownership of guns has ever been much of an issue, since violent crime and murder rates have traditionally been very low - and the Home Guard ensures quick and rapid defense of the country.