It depends. It is advisable to check with the specific countries embassy or consulate just to be safe if you plan on any traveling outside the country with a DUI conviction. The State Department can also be helpful in this regard. (I am sure there are countries that a DUI conviction would be problematic) Most countries - there probably won't be a problem. However, you do not want to spend lots of monies just to be denied entry when you arrive.
The exception is Canada where any DUI conviction can bar entry. (although waivers may be available - check with Canadian immigration attorney for the latest laws)
Also, if this is your second or subsequent DUI conviction you may be subject to the interstate compact. Interstate Compact You will need to check with an experienced DUI attorney on the latter.