Johnson, Jones, Scholes, and Carras (2013) published a review of research literature that mostly focused on the positive aspects of video gaming, which they argue have been overlooked due to dominant societal preoccupations with theories about its effects on violent behavior (Kutner & Olson, 2008; Ferguson, 2007; Ferguson et al., 2013). They include a section reviewing violent games specifically though, which I'll paraphrase here.
As others have already noted, existing research on relationships between video games and violence has been insufficient and heavily criticized. A relatively convincing study found longitudinal relationships between playing violent video games and being rated as more aggressive by teachers and peers (Gentile & Gentile, 2008). However, problems with other studies have included publication bias and unsupported generalizations from in-lab results to behaviors in normal contexts (Boyle, Connolly & Hainey, 2011; Ferguson, 2007; Kutner & Olson, 2008; Sherry, 2004, 2007) and dependence on self-reported subjective experiences (Lemmens et al., 2011; Möller & Krahé, 2009; Anderson et al., 2010; Shibuya, Sakamoto, Ihori, & Yukawa, 2008) or self-reported aggressive behaviours (Shibuya et al., 2008; Bucolo, 2010). Criticisms aside, two of these studies did not demonstrate any sustained causal relationships anyway (Lemmens et al., 2011; Shibuya et al., 2008).
After correcting for publication bias, Ferguson (2007) found no meta-analytic support for the relationship. Ferguson and colleagues (2013) later found no effects in their own study either, and claimed to have eliminated the likelihood of a false null result. Anderson and colleagues (2010) did one of those controversial meta-analyses supporting the relationship that's listed in the Wikipedia page to which @KonradRudolph's accepted answer links, but Wikipedia covers that particular controversy well enough already, so I'll leave it alone. Suffice it for here to say that Ferguson and Kilburn (2010) weren't convinced.
Johnson and colleagues (2013) also recommend Carras et al. (in prep), "For a more complete exploration of these issues and the research regarding long-term outcomes of videogame play," but it looks like they haven't completed their analyses yet at this time. BTW, I have cited Johnson and colleagues for a related answer on Cognitive Sciences about the addictive quality of gaming.
- Anderson, C. A., Shibuya, A., Ihori, N., Swing, E. L., Bushman, B. J., Sakamoto, A., Rothstein, H. R., & Saleem, M. (2010). Violent video game effects on aggression, empathy, and prosocial behavior in eastern and western countries: A meta-analytic review. Psychological Bulletin, 136(2), 151–173. Retrieved from http://lilt.ilstu.edu/mjreese/psy453/Anderson%20et%20al,%202010.pdf.
- Boyle, E., Connolly, T. M., & Hainey, T. (2011). The role of psychology in understanding the impact of computer games. Entertainment Computing, 2(2), 69–74.
- Bucolo, D. (2010). Violent video game exposure and physical aggression in adolescence: Tests of the General Aggression Model. University of New Hampshire.
- Carras, M. C., Johnson, D., & Jones, C. (2014). Adverse effects of videogame play on health, behavioral and educational outcomes in longitudinal studies of young people (unpublished manuscript). Further info available at http://www.crd.york.ac.uk/PROSPERO/display_record.asp?ID=CRD42012002882#.Uww4b4V5Pmw.
- Ferguson, C. J. (2007). The good, the bad and the ugly: A meta-analytic review of positive and negative effects of violent video games. Psychiatric Quarterly, 78(4), 309–316.
- Ferguson, C. J., Garza, A., Jerabeck, J., Ramos, R., & Galindo, M. (2013). Not worth the fuss after all? Cross-sectional and prospective data on violent video game influences on aggression, visuospatial cognition and mathematics ability in a sample of youth. Journal of Youth and Adolescence, 42(1), 109–122. Retrieved from http://static1.wikia.nocookie.net/__cb20131108072659/the-kings-hand/images/a/ae/Not_worth_the_fuss.pdf.
- Ferguson, C. J., & Kilburn, J. (2010). Much ado about nothing: The misestimation and overinterpretation of violent video game effects in Eastern and Western nations: Comment on Anderson et al. (2010). Psychological Bulletin, 136(2), 174–178. Retrieved from http://www.igea.net/wp-content/uploads/2010/03/Ferguson-Kilburn-2010.pdf.
- Gentile, D. A., & Gentile, J. R. (2008). Violent video games as exemplary teachers: A conceptual analysis. Journal of Youth and Adolescence, 37(2), 127–141. Retrieved from http://www.psychology.iastate.edu/~dgentile/pdfs/G2_Exemplary_Teachers_in_press.pdf.
- Johnson, D., Jones, C., Scholes, L., & Carras, M. C. (2013). Video games and wellbeing: A comprehensive review. Sydney: Young and Well Cooperative Research Centre. Retrieved from http://www.youngandwellcrc.org.au/document/ea0e9511fce02b8be23990_07ef7fc4c7/Videogames_and_Wellbeing.pdf.
- Kutner, L., & Olson, C. (2008). Grand theft childhood: The surprising truth about violent video games and what parents can do. Simon and Schuster.
- Lemmens, J. S., Valkenburg, P. M., & Peter, J. (2011). Psychosocial causes and consequences of pathological gaming. Computers in Human Behavior, 27(1), 144–152.
- Möller, I., & Krahé, B. (2009). Exposure to violent video games and aggression in German adolescents: A longitudinal analysis. Aggressive Behavior, 35(1), 75–89. Retrieved from http://www.vfa-ev.de/fileadmin/File/Moeller_Krahe_AB2009.pdf.
- Sherry, J. L. (2004). Flow and media enjoyment. Communication Theory, 14(4), 328–347. Retrieved from http://cht.tcm.ncku.edu.tw/attachments/053_96_Flow%20and%20Media%20Enjoyment.pdf.
- Sherry, J. L. (2007). Violent video games and aggression: Why can't we find effects? In R. W. Preiss, B. M. Gayle, N. Burrell, M. Allen, & J. Bryant (Eds.), Mass media effects research: Advances through meta-analysis (pp. 245–262). Mahwah, NJ, US: Lawrence Erlbaum Associates Publishers.
- Shibuya, A., Sakamoto, A., Ihori, N., & Yukawa, S. (2008). The effects of the presence and contexts of video game violence on children: A longitudinal study in Japan. Simulation & Gaming, 39(4), 528–539.