I haven't played many of the resident evil games, but I've been impressed with the few I've tried. I played the remake of the original with my brother (the gamecube version) and it was suitably creepy. The dated controls and fixed camera angles could get frustrating, but it had a much more isolated feel than later games that increased the level of unease.
Some time after that I played Resident Evil 4 (again for the gamecube) and it was a great experience overall. My favorite moment from that game was a shootout in a house I had barricaded. That was the first game I ever played where a head shot actually made things worse! I also enjoy the mythos from the games, with umbrella and big bads like wesker. And the large cast of characters offers a unique perspective for each game.
I don't play every game, but certain installments catch my eye. The most recent would be Resident Evil Revelations, where you're investigating a monster filled boat in the middle of the ocean. Still need to pick that one up.