It's already mentioned but yes, Siren for PS2 definitely. Only game that got into my subconscious and gave me real nightmares. I had to stop playing for a month and resumed it. I still enjoyed every minute of it.
Clock Tower on SNES and the sequel Clock Tower on PS1. I remember playing this with my sister who just happened to have the same name as the protagonist and has the same high school uniform. I used to drive her crazy by telling her it's a game about her. In the end, the PS1 version really creeped her out and she just ran off mid session.
Clock Tower 3 is memorable for several things. One...her best friend who looked exactly like Ron Weasley from Harry Potter (It was a constant joke when I played it with my sister). Two, like the previous games, the heroine gets chased by killers and evades them by hiding but then the last thing I expect happens. Eventually, she turns into a magical girl that reminds me of Akazukin Cha Cha Magical Princess Holy Up and obliterates them with magical arrows and a killer lightning atomic bomb from the heavens.
Alien Isolation was...unggh...this game had me on pins and needles the whole time. The Alien's AI is really terrifying and unpredictable. There seems to be no way to exploit it and the way it follows you and only you all the time is nerve wracking. I only wish I finished it but our PS3 broke down before I could.
There's this free downloadable horror game called Akemi Tan. It had a jump scare that was so unexpected and disturbing, my nephew played it and never touched it again.