Currently Online 
PS2: Onimusha 3, Haunting Ground, Ring of Red, Suikoden 5, Gradius V, Shadow of Destiny, Silent Hill 2 and 3, Espgaluda, Shadow Hearts 2, Valkyrie Profile 2, Ace Combat 4, Virtua Fighter 4 Evo, Speed Kings (Available on GameCube. Criminally underrated game), NFS Hot Pursuit 2 (PS2 version is different and far superior to the other versions), Resident Evil Outbreak File 1 and 2 were cool too but they're best played online which is no longer a thing officially. I enjoyed Clock Tower 3 as well but I don't know if I can recommend it. Consider it if you love Haunting Ground.
PS1: Zanac X Zanac, Jackie Chan Stuntmaster, Bugs Bunny Lost in Time, Bishi Bashi Special.
I'd recommend too many but the vast majority of them are available on at least PS3 as digital classics. I'll add more games as I remember them.
