Mark,
they vary widely and I don´t know about all European countries. Some countries allow more than others but basically all guns are registered (with the exception of single-shot shotguns that are still quite freely available in some countries). The UK situation you probably know. Finland has registration and police approval for purchase but you can get just about anything you want except full-auto which requires collector status. I understand Sweden is almost the same but there's a limit to how many guns you can own.
I think Germany has restrictions on military-style rifles and a system where you get a hunter's licence and can then buy 2 pistols and some long guns, and sportshooters must be members of approved clubs. France has some sort of calibre classification thing where certain calibers are more tightly regulated than others. Italy also has banned military calibers from civilians, but allows modified guns such as 9X21 and 45HP.
All this was off the top of my head, if anyone knows more please correct me!
