Fighting:
Tekken series, Soul Blade, Bloody Roar 1-2, Dead or Alive, Psychic Force (3D)
Street Fighter Alpha 1-3, Guilty Gear, Capcom Vs. SNK Pro - Millenium Fight 2000, some KOF ports (2D)
Driving / Simulation:
Gran Turismo (simulation) Ridge Racer (arcade), any versions
Radikal Bikers
Ace Combat 1-3 (air combat arcade-like simulator)
Omega Boost, Colony Wars (spaceship combat sims)
Action:
Metal Slug, MegaMan 8 / X3-6, Gunner's Heaven, Panzer Bandit (2D)
Klonoa, Megaman Legends - The Misadventures of Tron Bonne, Silent Bomber, Tail Concerto, Strider 2 (3D)
Sports:
Any Pro Evolution Soccer / Winning Eleven
NBA Live, Fast Break or Total NBA.
1 on 1 (very rare J basket game)
Everybody's Golf
Shumps:
Einhander, R-Type Delta, Ray(Storm Crisis), G Darius, Thunderforce V (3D)
Darius Gaiden, Gradius Gaiden, GaiaSeed, Harmful Park, Raiden (any), SDF Macross - Do You remember Love (2D)
Adventure:
Metal Gear Solid
Silent Hill
Resident Evil series (I don't like them too much though)
Galerians
Tenchu
Hope it helps