Resident Evil 2 was one of my favorite games of that generation - played it and beat it in both Leon and Claire's main and alternate playthroughs. Code Veronica needs a special mention as it was a massive and ambitious entry into the series, the first one in full 3D prior to RE4.
My dad picked up Resident Evil when it came out and I would stay up on the weekends and watch him play so, RE 1 holds a special place in my heart. I like them all though, even the spin-off titles. I'll never forget popping in the Darkside Chronicles for my little cousin (she got that one first and it was her introduction) and she asked me; "Who is that guy and the lady with the red hair?" She loves the concept of the games so, I'm getting her started from the very beginning this summer.