It seems that everyone is on the same page with their advice here, and I agree with them. Try something a little different. There have always been platformers and action/adventure type games that are centered more around puzzle elements, which require one to find some solution to a problem before they can move on. The Zelda series is the most popular example, but there are plenty other games that require some kind of thought process in order to advance. Sure, there are killing in those games, but it's more figuring out what to do next that impedes progress. Well, and bosses, but they usually require some kind of strategy to defeat too, which ties into the puzzle part of the game.
Maybe you could try something different entirely. Something that doesn't involve any killing at all. Double Fine's Stacking is all puzzle, with no violence. It involves figuring out things like how to end a party, or how to close down an exhibit, so that certain people will end up doing something else important, and each puzzle has multiple solutions, each more difficult than the last.
I recommend Flower to anyone who has a ps3. It's one of those games that's more like an abstract piece of interactive art. It doesn't speak to everyone, but it provides those it does speak to with an experience that's like no other. Though I usually hate the use of motion control, Flower could only work with the use of sixaxis, which is my favourite motion control peripheral, if I had to choose one, simply because it doesn't involve too much excessive movement. The sixaxis controls in Flower suit it so perfectly, and somehow manage to break down the fourth wall and make the player feel more immersed in the game, that it just wouldn't feel right any other way.
Right now I'm devouring a visual novel called Katawa Shoujo which is free to play for everyone who has a working pc or mac. There's very little "game" there, so it isn't for everyone, but I still recommend giving it a try, especially since it doesn't cost anything, and is quick and easy to set up(this coming from someone who isn't remotely tech savvy). Here's its site: http://katawa-shoujo.com/
Well, I hope you can find something that satisfies you. I know it's getting harder and harder this gen to find quality games. They exist. You just have to dig deeper, since the surface is crowded with fps and ultra violent hack and slash games. The downloadable service on your system of choice is a good place to start, because that's where a lot of unique games live. With physical games, you might want to do a little research beforehand, so you know what you're getting into. You did take the right step by asking people on a message board. If you can't trust your online community to give some good recommendations, who can you trust?
It also helps if you can find a reviewer who you generally agree with, which can be difficult with the majority being biased towards fps, or being paid off to give a game an inflated review score, and not at all impartial. Hopefully you can eventually get to the point where you have some idea as to whether or not a game is your cup of tea without having to do any research, or depend on reviews at all, but it took me a while to get to that point, and I'm sure it'll take you a while too. Well, good luck. I hope we have been helpful.