In the UK, where handguns have been completely illegal since 1997, handgun crime has increased from 2,687 (1998/1999) to 4,347 (2004/2005).
(Source: British Home Office,
http://www.homeoffice.gov.uk/rds/pdfs06/hosb0206.pdf)
It's common sense. The more difficult it is for regular citizens to get a gun, the more incentive criminals have to get them, because they know that they won't ever have to confront armed citizens.
Remember: making guns illegal will make criminals stop using guns, just like making drugs illegal has stopped drug addicts from using drugs.