None have changed my life nearly as deeply as they have changed yours, though some of them have certainly changed my perspective. The change in perspective has likely led to me making somewhat different decisions than I would have otherwise, and has actually led me to make a friend or two, too.
For example, playing Phoenix Wright for the first time gave me a whole new outlook on what video games could be; up to that point I had played primarily JRPGs and platformers. I have since played many different games and looked for deeper meanings from them than I ever got out of (most) of those others, and am better for it. Games are an artistic medium to me now, and I'm not sure that they were before.
Playing Phoenix Wright and loving it so much probably swayed my decision to play Katawa Shoujo. When I played Katawa Shoujo, I had just experienced a pretty terrible breakup followed by two pretty traumatic weeks. I don't want to get into too many specifics, but lets just say that I have very poor taste in coping mechanisms and wound up spending a night in jail while not even being aware enough of my surroundings to know where I was. Bad shit. Needless to say, after coming to, I realized I needed to get the fuck out of my situation and moved far, far away from where I was. The thing was, when I did move away, I was lonely. After a pretty long period of feeling this loneliness, I say someone mention Katawa Shoujo, and entirely free of any context for what it was decided to give it a shot. Literally the only thing I knew about it was that it was a "dating sim". I know now that that's not what it actually is, but back then I didn't really know the difference between that and a VN. I quickly realized what it was, and I may have even been ready to turn it off and move on. Then I saw Hanako. I've posted this in many places, but Hanako and I share some similarities, both physical and personality-wise.
This all lead to me being completely overwhelmed by emotion at the end of the route. I had to say something to anyone about it. So I posted a user blog about it on a certain gaming website that I frequent. Someone sent me a personal message in response, and I've kept in contact with him ever since. Having that person as a friend has been one of the only things keeping me sane in the lonely place I'm at right now.
So, Katawa Shoujo made me a friend, and opened my eyes to a whole new genre of game, which has in turn opened my eyes to another level of being able to accept people for who they are. I'm now into something that gets a really bad rap from people who don't understand it. Because of that, I've learned not to make those assumptions about other people, or the things they like.