There are plenty of classic shooters that are still amazing. Before the Playstation generation obviously:
Half Life 1 and 2, Counterstrike, Battlefield, Doom, Wolfenstein, Duke Nukem, Unreal Tournament and the original Halo are still amazing to this day.
JRPGs? There are only a few that are classic to anyone other than the genre fanboys - Final Fantasy series, DQ series, Chrono Trigger/Cross... not much else worthy of note.
I can't really answer this question as every genre has classic games that don't age.
Xbox Gamertag: BrapRedHarvest PSN ID: Brap123