Resident Evil 5
For whatever reason growing up I don't recall hearing anything about the franchise; I suppose my family and most friends I knew had Nintendo systems. Even when we got the GameCube, I don't remember anything related to ReMake at all despite its prestige and fitting snugly in the launch window. I would see Resident Evil 4 at Blockbuster, but for whatever reason it never really drew my interest; I would say the M rating might be part of why, but I played other M games so that wasn't the issue.
It wasn't until the demo for Resident Evil 5 became available on Xbox 360 years later that I got my real first taste. I don't recall exactly why I downloaded it, though it must've been a combo of the logo and how the game looked - still looks great IMO, but I must've ended up replaying it at least a dozen times prior to launch. Even as a co-op game, I treated it as single player and really liked it regardless. Sheva was cool, and while slightly cumbersome to deal with, the AI was never a dealbreaker for me. I wasn't really scared at any point, but it was certainly tense and a challenge. And while I really liked 5, it didn't hook me in to the franchise. While Operation Racoon City looked interesting, I never ended up playing it, and 6 didn't appeal to me either.
It wasn't until years later watching Gametrailers that I paid more attention to the franchise. I started watching them stream a lot starting around the spring of 2015, and eventually they streamed Code Veronica, 4, and 0 which I watched and enjoyed. During 4, Brad and Huber mentioned the demo was that opening village section which struck me as funny as that is the same exact demo situation as 5 that I enjoyed so much. The second game I ended up playing was Resident Evil VIII, and have since played Zero, ReMake, RE2R, RE3R, and Village as well and consider RE to be one of my favorite franchises.
I know people have issues with 5 but I stand by it.