The research actually shows a correlation between games and a decline in violence, but Stetson University's Christopher Ferguson says that's probably coincidence. Importantly, what his study does show is that there was definitely no rise.
Ferguson conducted two studies, detailed in this report. The first examined "movie violence and homicide rates between 1920 and 2005", the second looked at "video game violence consumption and its relationship to youth violence rates from 1996-2011". The key thing he found was that "societal consumption of media violence is not predictive of increased violence rates in society".
The first study found no correlation between violence in popular movies and homicide rates overall, bar a brief correlation in the mid-20th century, something Ferguson suggests may be behind the original idea that media could affect behaviour. The look into video games actually correlated "strongly" with a decline in violence but Ferguson was at pains to say this was likely coincidence.
"This research may help society focus on issues that matter and avoid devoting unnecessary resources to the pursuit of moral agendas with little practical value."
The report points out that most studies usually involve laboratory tests for aggression, using some bizarre methods, rather than looking at "real-life exposure". I'm sure this is going to get both sides of the argument thumping tables but Ferguson makes a really important point here: "Society has a limited amount of resources and attention to devote to the problem of reducing crime. There is a risk that identifying the wrong problem, such as media violence, may distract society from more pressing concerns such as poverty, education and vocational disparities and mental health. This research may help society focus on issues that really matter and avoid devoting unnecessary resources to the pursuit of moral agendas with little practical value."