If you have been convicted of any crimes in the past, your opportunities for entering another country might be limited.
There is no single authoritative source to consult on travelling with a criminal history, but information can be found either on the destination country’s immigration agency website, through its embassy in your homeland, or by searching legislation.
Many countries do not easily welcome those with criminal backgrounds for obvious reasons, but what criminal history is relevant, and the period that must have elapsed since a conviction, varies from country to country. For some countries, particularly Canada and the US, even a minor criminal conviction 50 years ago can cause you to be refused entry, while others would require a conviction for a violent or serious crime to be refused entry. This page also lists ways (if known) to overcome a bar on entry due to a criminal history.
In general it is very difficult, if not impossible, to travel to any country if you have a record of convictions for violent or sexual crimes, repeated convictions for felonies, or a recent conviction for a serious crime. Some countries prohibit their own citizens from leaving if they have serious criminal histories. However, in general, authorities are not concerned about petty offences.
If you are on probation or parole you must follow the travel policies set by your probation officer to the letter, as leaving the country (or even your locality in certain countries) without permission will result in a violation. Generally offences committed in the destination country count more than offences committed outside of their country. The most common question on visa forms and arrival cards is if you’ve formerly been deported or refused entry from the country (and often whether this has happened to you in any country).