In short, yes. Each country has the power to control its boarders, and to make decisions about who can and cannot enter the country. For this reason, it’s critical that you contact the location you plan to visit and get information about your ability to travel there related to any convictions you may have.
The United States and Canada, for example, have an information-sharing agreement that gives each country access to the other’s criminal records and public safety information – this includes access to the Canadian Police Information Centre (CPIC). CPIC is a database that all Canadian police officers, including the RCMP and National Police Service, as well as the Correctional Service of Canada, can access and search. A search of this database is conducted using an individual’s name and date of birth, and includes access to criminal records, non-conviction records, cases under investigation, intelligence information, motor vehicle and driver information, and the Alzheimer Wandering Registry.
Other countries may also have access to the CPIC if they are a registered partner, and the RCMP shares CPIC information with foreign authorities who may save the information and use it to make a determination on an individual’s admissibility. It is best to contact the specific location you intend to travel to get information regarding their treatment of certain types of records prior to initiating any travelling.