Yes. Some countries, including Mexico and Canada, may refuse to allow you to enter if you have a recent DUI or another criminal conviction or pending charges. Furthermore, the U.S. Department of State will generally refuse to issue you a U.S. passport if you’re convicted of certain felony offenses.
Canada makes people with DUI, drug or other convictions jump through hoops to enter the country and obtain permission from the Canadian Government. For a temporary stay in Canada, you might have to get a temporary resident permit (TRP) in order to enter the country. This requires you to pay an extra $200 (Canadian) processing fee and to prove that your reason for going to Canada is justified. Even then, there is no guarantee.
There’s an alternative method, which is to restore your admissibility to Canada. This requires at least five years to have passed since your conviction. After that, you must submit an application to show you have been rehabilitated and meet certain other criteria. In the end, it may simply be impossible to travel to Canada with a felony conviction.
Mexico may deny you permission to enter if you have committed any crime defined as “serious” under Mexico’s laws. A serious crime is one that has a significant, negative impact on the fundamental values of society. DUIs may or may not be treated as a serious crime by a border agent, and it may depend on the circumstances surrounding the DUI as to whether it was a major DUI offense and considered a serious offense by Mexican authorities. All drug crimes are considered serious in Mexico, and it can be virtually impossible to cross the border if you have a conviction for these or other serious crimes on your record.
What about getting a U.S. passport?
The State Department can deny you a passport if you have been convicted of certain felonies. Some of those include, for example, money laundering and sex offenses that require registration. You can also be denied a passport if you have a current felony warrant or if you are on parole or probation and the conditions include remaining in the area.
Importantly, any state or federal drug felony involving a passport or an international border will generally keep you from getting a passport. The State Department may also refuse to give you a passport after a misdemeanor drug conviction where you used a passport or crossed an international border.
After you have served all your time, you can petition the State Department to overcome the denial of a passport. However, it can be a real challenge.