By far the first Resident Evil is my favorite.
I remember going up to Funcoland everyday when they got their shipments in waiting for it to be released. I can't even remember how often it kept getting pushed back, this was before games had release dates on every Tuesday (US) My friend that worked there, my brother and I were super psyched once we got it.
I would always get into arguments with friends over which one was the best, but realized it was generally always the first RE game they played that's their favorite, fortunately I was able to get the first one on release while the majority of people I know got into RE when they released the second one.
To me the whole creepy mansion was just awesome, it seemed way scarier than most of the environments/areas in other RE games.
Edit: I should also give Resident Evil remake an honorable mention since it was almost as amazing as playing the original for the first time, and the graphics still stand up to this day compared to the original.
Had posted this in the Collectors Thread in the General section, but heres my collection of RE games (except not pictured my PS1 RE games, RE0 and OutBreak 1 & 2) and then obviously the PSN downloads and Code Veronica/RE4 for GoD.