Ohhh, this is a tough one...
Here's my PSX list
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Klonoa
Crime Killer (bad game, but literally has a "60 fps" sticker on the jewel case)
Devil Dice
Einhander
R-Type Delta
Thunder Force V (PSX + SAT)
Ridge Racer High-spec
Elemental Gearbolt
Motorhead
N2O
RayCrisis & Force
Internal Section
There may be a few others, but at the moment, that's what I can think of. I will do an N64 and Saturn list as well.
People always bring up Wip3out, but the truth is, Wip3out did not run at 60 fps nor use any sort of high resolution mode.
2D games across all systems mostly ran at 60 fps (including those with 3D elements). Also, most RPGs (especially Square titles) used 60 fps elements in various aspects of the games (menus, in particular). Not really 60 fps games, of course, but elements were included. I always found it interesting how the menu in the FF games, for instance, ran at 60 fps even in battle (while the 3D portions were much lower). NiGHTS on Saturn had a similar thing going on, where the 3D portion updated at 30 fps and the 2D backgrounds moved at 60 fps.