I have been living in Japan for 4 years. The past two years I have not filed taxes. I do not owe any money, but am worried that I will be unable to renew my passport from abroad. If I don't owe any money to the IRS, would it be OK to apply for renewal? I am in the process of filing for those two years, but need the passport urgently.

You must file all your tax returns.

If your total worldwide income exceeds the filing requirement, you must file your U.S. tax return. On your return, you must report your world wide income. If you paid taxes in the foreign country, you will claim credit for taxes paid in the foreign country by filing Form 1116 or can file form 2555 Foreign Earned Income Exclusion.. Even if you have a filing requirement, the chances are you will not pay any U.S. tax or pay very little U.S. tax.
Another filing requirement is Form TD F 90-22.1. Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income

Renew your passport; don't worry about it.

Whether you file or not probably will NOT affect ypour passport renewal.

However, you SHOULD file the return if your income meets certain minimum levels.