I had been living under a rock for quite a while, so the concept of flesh-eating zombies was actually new to me by the time I came across Resident Evil. The first thing I saw of it was an article about RE3 in a little booklet that came with a Tomb Raider game I had bought, and I immediately fell in love with the idea of guiding a woman in a cool outfit through a scary city full of zombies.
The funny thing is, I didn't really get into videogames until the late 90's, the only other game I knew was Tomb Raider, and for some reason I expected all games to be the same. So when I first played RE3 at a friend's house, I was surprised that Jill wasn't able to jump around and climb walls like Lara Croft, and that there was no tutorial level set at her home. But I got used to it rather quickly and, needless to say, I liked this "new" kind of gameplay too.
The first RE I owned myself was the original RE1, which I have some very fond memories of. I played as Jill first because I already knew her from RE3, and didn't switch to Chris until I had completed the game at least five times with Jill. I spent hours trying out every possible combination of actions and decisions to see how it would affect the story and the ending: What if you solve the shotgun puzzle yourself without requiring help from Barry? What if you save Rebecca, don't save Rebecca, or completely avoid going to the room where she's attacked by the hunter in the first place? Can you get away with NOT saving Chris from the poison/Plant 42 and then continue the game as Rebecca? And so on...
Then I got my hands on RE2 and enjoyed it just as much. It didn't offer as many plot-altering decisions as the first game (or rather, none at all), but the concept with the two scenarios was cool too, and I loved all the new characters, even Leon at the time. I could go on and on about how every new installment of the series managed to enchant me in its very own way (well, except RE4, I hated that one), and how just thinking about it fills me with nostalgia, but I think you get the idea.
Happy 20th birthday, Resident Evil!