No one game has ever changed my life positively, but I suppose these are the closest instances:
Early Pokemon games (Gen 1 & 2 stuff, so R/B/Y, Stadium, etc) were enthralling to me as a kid, I couldn't get enough for a long time. Sure, I was obsessed with Sonic and TMNT too, but Pokemon was on a different level.
TellTale's The Walking Dead, especially the first season, was the first game where I actually felt anything for a fictional character, a notion I had previously scoffed at (for any type of media). Lee was really great, well written and voiced.
Chrono Trigger was not the first RPG I played but it was what completely shifted my video gaming preferences from whatever junk I could get my dumb kid hands on toward higher quality games. It is why I really have very little interest in simple stuff like racing or classic arcade style games, they can't provide rich enough experiences (though they can be neat here and there).
Super Street Fighter II Turbo HD Remix was kind of like Chrino Trigger to me in that my preferences skewed heavily toward the fighting game genre because of it. I think any game that can alter your entire interest in the medium is significant, and rare (at least for me). It wasn't like I never had an interest in the genre before it, I was even well acquainted with Street Fighter II before HD, but something clicked with me (probably because I'm pretty dang good at it).
Journey made me consider games as art. I never really thought about that, dismissed the entire notion as a stuffy douchebag thing to even consider, but it is a true masterpiece. It belongs in a museum alongside any other art, not just a video game museum. It's a modern art form, the natural evolution of traditional still imagery (might not entirely replace it since the interactive aspect isn't necessarily always desirable when wanting to view art).
I guess nostalgia is also a major thing for me with video games. I remember my childhood really fondly, and since I played a lot of games I associate them with better days. Maybe it doesn't count since they didn't change my life as a kid, but they're woven into some of my best memories which comprise my life.