At Hogwarts, there are four houses: Slytherin, Gryffindor, Hufflepuff, and Ravenclaw.
Do any of the other wizarding schools, like Durmstrang or Beauxbatons, sort their students into separate houses?
There is no known canon evidence that any of the other wizarding schools have a house system like Hogwarts does. The house system in general is pretty endemic to the British, though, from what British friends have told me, whether it's boarding or day school (I believe the British call what we Americans refer to as "private" schools "public" schools -- hopefully any British user will correct me if I'm wrong.). So the house thing is specific to the UK, if I understand correctly. However, going back to canon, unless there is more information on Pottermore that I just haven't gotten to yet, there is just no indication that any of the other schools use the house system. Is it possible? Sure. Is it proven? No.
Yes, the American school of magic has houses.
In a new piece on Pottermore, JK Rowling revealed that Ilvermorny, the North American school of magic, was heavily influenced by Hogwarts and included the idea of four houses:
This idea caught Chadwick’s and Webster’s imaginations. The boys’ ideas of what a magical school ought to be like were based almost entirely on Hogwarts, so they insisted that it ought to have four houses.
The school draws other aspects of its house structure from Hogwarts:
Lots more detail in the Pottermore article.
The four houses of Hogwarts were named after the four founders of Hogwarts (not founders of Wizarding education or something global). So, it's safe to assume that houses of other schools had different names (probably bearing names of founders of theirs). It's also a possibility that other schools didn't have houses.
Note: The canon never mentioned houses of other schools. This is the best guess based answer I can think of.
Possibly not because boarding houses are speciality of the United Kingdom and maybe some of its former colonies. It may function like that in Northern America, imitating all the Ivy League schools for muggles. But no; Hogwarts uses a distinctive "class" system that marks the whole British way of life. I really cannot see e.g. the French imitating the British, since they used to be mortal enemies in the past. Also, the Brits are very uptight, especially those in academic fields, while other european countries prefer more freedom when it comes to managing students. So NO, I don´t really think that other countries have schools with separated Houses like Hogwarts.