Yes, but you need a visa. (US citizens also need a visa for Australia. In fact, everyone except citizens of Australia and New Zealand needs a visa for Australia.)
Yes, US citizens can travel to Japan.
Yes, US citizens can travel to Singapore.
Yes, US citizens can travel to Uzbekistan.
Yes, US citizens can travel to the Philippines.
Yes, US citizens can travel to New Zealand.
It is not necessary a visa for the citizens of Australia to enter in Romania.
No, US citizens cannot travel internationally without a passport.
Yes, US citizens need a visa to travel to Kazakhstan.
Yes, US citizens need a visa to travel to Russia.
Yes, US citizens need a visa to travel to Uzbekistan.
No, US citizens are generally not allowed to travel to North Korea due to travel restrictions imposed by the US government.