I consider Fallout my all time favorite series, following Mass Effect, The Witcher, and Halo.
With the exception of Halo, do all of the series have much in common. RPG series that have excellent story telling, the freedom of choice for the player to decide how the story changes that will lead to different outcomes and consequences, a well written universe full of detail and lore, and on top of all of it can it manage to deliver enjoyable gameplay (both the original Fallout games and newer styled ones). Halo on the other hand, although it's no RPG by any means and is rather linear in story telling, I consider a favorite for being a fun shooter capable of having a good story and an extraordinary universe that has expanded the franchise into more than just video games alone.
Other series I enjoy and are worth mentioning are the Shock games and the Red Dead series. However, I cannot consider them as favored for me as those mentioned above. For the Shock games, the System Shock series by itself is all around fantastic. With the Bioshock series however, do I consider the first game very good but it's the only game of the series that I actually cherish dearly as I find the later games in the series unable to live up to it (Bioshock 2 in terms of story, Bioshock Infinite in terms of gameplay and all around lack of elements that make a Shock game). I enjoy Red Dead games but it was mainly Red Dead Redemption that created my love for it. Although Red Dead Revolver is also a good game on its own terms. Still, both of these series have at least one game I consider to be one of my most beloved games ever, Bioshock and Red Dead Redemption.