[ChEEbA]

There was a game on dreamcast called "carrier" that was similar.
On dreamcast also, there was illbleed - both of these games were really scary and fucked up.
On the more action based side - "sword of the beserk", and one called "renegade".
In fact, if you can get a dreamcast in working order (some companies online actually sell them brand new, and boxed still), I'd highly reccomend it. People are ebaying games for next to nothing also...I maintain, in the short life span of this console...one of the finest games libraries I've EVER seen was available.

On PS1?
Deathtrap dungeon, nightmare creatures 1 & 2, clock tower 1 & 2, alone in the dark, alone in the dark: the new nightmare, the resident evil series, parasite eve 1 & 2, oh, and of course the first 2 silent hill games.
And, not really horror related, but quite good all the same was one called "chase the express", dino crisis was "ok" but part 2 was WAY better...
***Just remembered - Evil Dead: Hail to the king...I SO looked foward to this game, but found it to be a huge dissapointment.
Those are all I can think of right now, but there ARE more.

PS2:
Onimusha, res evil outbreak 1 & 2, Silent Hill 3 & 4, Fatal Frame...other than that I'm not too familiar.
***Also just remembered Evil Dead: A fistfull of boomstick, which was much MUCH better than the evil dead game on the ps1.
There was a pretty cool looking disaster survival/govt conspiracy type game also, but I can't remember the name...good luck.