I have had my favorites changed a lot of times. Leaving out the multiplayer games out of this story, I would like to start with Mass Effect.
Why? Well, the story and choice making has always intrigued me in the gaming world. Sure, ME 3 might have not ended on the brightest note compared to the first two games, but it was a really nice series. I was actually avoiding it at start because I am not a really big fan when it comes to space games. I thought it would just be boring, flying a spacecraft, shooting other spacecrafts and such things, but when I finally laid my hands on it, I couldn't stop playing. In fact, I finished each title the very first day it came out.
Second series that I loved even more were Metro games. I always loved post-apocalyptic genres and Metro was really unique. It also had choice & consequence system, although that didn't really matter that much in the end when it comes to the first game since the story of the second game starts the way it starts. It has nothing to deal with your choices in the first game. But it surely did have a good choice & consequence on its own. And quite a nice moral story behind it, too.
And my current and probably all time favorite - Witcher. I have played the first 2 titles before, I liked them, but I never gave them that much of a thought. When Witcher 3 came out that completely changed my perspective towards the entire game series. It is a well polished gem and I bet nobody will get even close to beating it when it comes to the storytelling, actor development & choice and consequence system. It is an absolute masterpiece. And not just the game itself. The DLC's were so amazing that I was actually surprised how much detail they put in those as well.
Notable mentions I would like to add here as well - TES, Fallout.