Yes, indeed most major private railway (especially in the Kansai Area) run on standard gauge.
The full list (off the top of my mind) is Keikyu, Keisei, Hokuso, Shin-Keisei, Chiba Newtown Railway, Shibayama Railway (and the Chiba Rapid Railway, absorbed by Keisei in the 1990s), the Hakone-Tozan...