In the realm of Japanese exclusives, I enjoyed "Insectorwars". It's a first-person shooter with cutesy insectoid enemies where you roam mazes. I haven't played it in probably fifteen years, but I remember it being very "Faceball 2000-ish".
I also really enjoyed Quarantine. It's not truly exclusive, as it received PlayStation and Saturn releases under different names in Japan, but it's a console-exclusive to the 3DO in North America. The soundtrack had a ton of cool grunge and rock acts from Australia, a lot of humor, and the concept was basically Crazy Taxi in a Post-Apocalyptic world.