Full disclosure: I’m a gamer, so I may be a bit biased here. However, I think I might be able to offer a unique perspective on gaming and gaming culture that those who are not familiar with them, but have only read about them secondhand, cannot. I’m also new to the Church, so I admit I still have a lot to learn.

Take what I say with a grain of salt.
I think the posters who say that games are not objectively sinful, but have the potential to be sinful for some, are onto something. The truth is that there is no evidence that games cause people to become more violent or more desensitized to violence, aside from isolated incidents like Columbine, which was more likely caused by the shooters’ pre-existing psychopathology.
To answer the question about Battlefield: kids, especially boys, have been acting out war games in imaginary play eons before video games were even a concept. I can’t imagine that too many parents in the 60s were that concerned that their sons were playing “battlefield” using capguns and toy swords in the backyard. I don’t think that actually seeing the violence on screen would that make that much of a difference (Battlefield doesn’t have a whole lot of gore, anyway). I think a bigger moral concern is some of the culture of the online community. Anyone who owns these games and a subscription to the service (Xbox Live or similar, depending on the platform they use) can play these games online with strangers, and the culture surrounding online gameplay isn’t exactly very edifying. A lot of people cheat using modded lobbies or hacked consoles (I think this is worse with Call of Duty than it is with Battlefield, though). People verbally abuse each other on the voice chat and messaging features. I’d be more concerned about stuff like this than I would be about the content of the actual game, especially when it comes to letting impressionable children play them. But if you are strong enough in your faith to resist temptation, avoid cheating, and always treat other gamers with respect, perhaps you could even be a “witness” to other people who play the game.
I think other games are a different story. I may be in the minority amongst gamers here, but I think that the ESRB ratings are usually there for a good reason. Most M (mature) rated games are M rated games not just because of gore, but because there is some other thematic content that children aren’t old enough to handle yet. For instance, I play a series of M rated games called Fallout, which depict a post-apocalyptic wasteland that is deeply scarred by the horrors of nuclear war. Lots of violence and lawlessness with frightening, disturbing content. I think it serves as a good warning of what could happen as a result of senseless, unjust war. I don’t believe it would be appropriate for a child, or even a young teenager, to play this kind of game because it might skew their view of the world if their moral compass isn’t well-developed. The series can, however, be suitable entertainment for adults who are well grounded in their morality, and sometimes it even sends a “good message.” In Fallout 3, the player character’s parents were scientists who, inspired by Revelation 21:6, made it their personal life mission to build an advanced water purifier to provide free, clean water to the people of the Wasteland, where clean water is scarce and most people only have irradiated, dirty water to drink. Without getting into too much detail or revealing any spoilers, the player can choose to be good or evil, and to save or sabotage the project, but it is clear that the parents are the good guys. The game glorifies selflessness and personal sacrifice and really berates and guilt trips you if you do anything evil. The other games in the series have more moral ambiguity, but your actions still have consequences. I actually don’t really know of that many games where evil is outright glorified, even if it is an option the player can choose, except perhaps the Grand Theft Auto series, which I haven’t played.
There’s also the psychologically addictive aspect of certain games that is pretty misunderstood. I would never touch the game World of Warcraft because I have a somewhat addictive personality and couldn’t trust myself not to get so sucked into it that it takes over my life. I know a man whose life was ruined by that game; he lost his job, marriage, and child, rarely pays his bills except for the internet bill and his WoW subscription, and barely even takes breaks to shower and sleep. It’s heartbreaking. But I know other people who play the game as a hobby and don’t let it take over their lives. Good for them, but that doesn’t mean everyone can or should.
I know people have said that there is a difference between violent movies and books and violent video games because the former are passive and the latter is active, but again, there are no controlled studies to back up the assertion that this makes even a bit of difference. Most people can distinguish fantasy from reality. In fact, I would argue that video games are a more productive way to spend your time than watching TV, because they stimulate your mind and can help with perception and critical thinking skills. Does this mean they cannot be potentially harmful? Of course not. If playing Battlefield is, in fact, desensitizing you to violence, negatively impacting you socially, or taking over your life so much that you rarely spend time doing anything else, then perhaps it might be mortally sinful for you and it’s time to put down the controller or keyboard and reassess your priorities. Otherwise, carry on, but constantly evaluate yourself and make sure games stay something positive for you, rather than something that hinders you spiritually, morally, or socially.