Most countries allow entry to U.S. citizens who have been convicted of a felony. The only document you are likely to need is a U.S. passport. Countries that require travel visas may ask for your criminal record on the application form. They may also conduct a criminal background check during the approval process. Several countries will deny you entry based on this information.
You must apply for a Tourist Visa (subclass 676) for permission to visit Australia if you have a criminal record. Australia assesses all individuals requesting visas against a list of character requirements. You automatically fail the character test if you have a substantial criminal record, including a prison sentence of a year or more, multiple convictions or a conviction involving escape from immigration detention. The authorities can still approve your visa application at their discretion.
Canada can deny entry to anyone with a criminal record. "Criminally inadmissible" offenses include driving under the influence of alcohol or drugs, commission of a crime punishable with a prison term of 10 years or more under Canadian law and involvement in organized crime. You may still be allowed to enter Canada if you are deemed to be rehabilitated or were granted a pardon.
You need a visa to visit China and you must disclose your criminal record on the application. The Embassy of the People's Republic of China does not expressively forbid entry to individuals with felony convictions. However, China requires visitors to register with the police after arrival and there are severe penalties for violating the terms of your visa.
You do not need a visa to visit Japan for a stay of 90 days or less. Visas required in other situations will be denied if you were imprisoned for more than one year or have a conviction involving drugs. Russia requires a visa for entry and you must list your criminal convictions on the application. The U.K. Border Agency conducts background checks on travelers before they arrive. Immigration officers can deny entry to anyone who they believe should not be in the U.K. or intends harm.
You can usually obtain a U.S. passport despite having a criminal record. The State Department can deny or revoke your passport under certain circumstances. These include having an outstanding federal arrest warrant, a court order forbidding you to leave the U.S. or conviction of a federal or state drug felony committed while using a passport to enter another country.
The legal requirements for entering another country frequently change. If you are denied entry at the border, you could be forced to return to the U.S. immediately. After you are allowed into the country, a foreign government may still conduct a background check and require you to leave in the middle of your trip. Always consult the embassy of the country you plan to visit to discuss your individual situation before leaving the U.S.