I'm on H1b and already got my US entry stamping when I went back to Taiwan last year. My H1b, entry stamp, and Taiwanese passport are all current. Can I travel to other countries (and enter US) without having to apply any visas?
I plan to travel to Mexico and Japan. What documents or procedures do I need?
Thanks!

You should check with the consulate of both countries whether you would need to apply for visa or not.