This would probably be a good time for me to take notes, as I passed the PS1 generation.
Some of the games people have suggested are inferior versions that really wouldn't be worth playing. Take for example, the entire marvel vs. series on PS1 was gimped. The series main attraction was being able to tag, but due to the PS1's lacking ram, that entire feature was removed from all the games in the series that appeared on PS1.
Mega Man Legends 2. For me, the best aged 3D graphics game on PS1. My original PS1 copy was stolen, so I now play it on PS3, but it's still great... Apart from Mega Man's voice.
Resident evil 1, 2 and 3
Mega Man X4
I can't recommend x5, or x6, because X6 wasn't supposed to be made, and visually looks and plays terrible. X6 also has extremely high difficulty-- not due to creativeness, but out of poor stage design layout and enemy placement. Not actual difficulty of trial and error. It's all just memory and random luck when it really pushes you.
X5 just doesn't have the same creative standard that X4 had.
Can't suggest Mega Man 8 because the superior version is on Sega Saturn with added features and more enemies.
That's all I've got without booting up my consoles.