A lot of countries don't allow people with a criminal history into their country. However, whether you can fly with a criminal record will depend entirely on where you're travelling to and how much time has passed since your conviction. The best way to find out whether you can fly with a criminal record is to visit the nearest consulate or embassy of the country you're visiting or to go on the website of their immigration office.
Here is a general overview of how strict each country is:
The USA has a strict policy for criminal records. They require you to answer truthfully on to all questions on your criminal history, even if you've completed the time on your conviction or your conviction has been pardoned. If you're from a country that distributes the Visa Waiver Program and have a criminal record or are in the middle of a case determining your criminal record, you will be ineligible for the Visa Waiver Program. Similarly, if you're from a country that usually doesn't require a visa to visit the USA, you might be refused entry based on your criminal history.
Canada has one of the most strict policies on criminal records in the world. However, you make an application for 'rehabilitation', which might make getting into the country easier. You can be eligible for rehabilitation if your the time passed since your conviction was cleared is more than 10 years and the crime you committed has a prison sentence less than 10 years in Canada
China's criminal record policy is varied. Contact your nearest consulate or embassy with details of your criminal record to find out if you're eligible to visit
As a general rule, countries within the European Union will allow you access into their if the crime you convicted resulted in less than a three-year sentence.