The short answer is: some countries will, and many won’t. For instance, Mexico’s industrial property law allows for material that has been patented in the United States to be patented in Mexico as well, provided that some other technicalities are accounted for. Canada tends to grant patents to claims that were granted in Europe or the United States, but there is no statutory framework that compels Canada to do so.
In contrast, Australia and New Zealand are entirely indifferent to what any other country considers to be patentable.
In some cases, particularly technology areas that have backlogs at the USPTO—a patent attorney can advise you as to what these areas are—it can make sense to file an International Application in the United States.