Metal Gear Solid was made for analog in mind.
Ape escape specifically as it required dual shock to play.
Other games like FFVIII, Resident Evil 3, supported analog and they released games like Resident Evil 1 and 2 with analog controls. I'd say the majority of psx games released from 1998-1999 to the end of its life cycle supported analog. Maybe not the right stick, but the left stick definitely.