Stories about origin are always different from culture to culture. I would suggest examining "The World on the Turtle's Back" as an origin story in comparison to another culture's stories of origin. Folk tales, as mentioned above, are also great stories to use in comparison with other cultures.

I had a class in college that discussed the similarities and differences in all the Cinderella stories throughout the world.  We got a hand-out of pictures showing the different types of shoes that the girl would wear from that nation. It was certainly interesting to see the "rags to riches via a man" theme evident in all of them. But the endings and situations are certainly different and fun to read. Just Google Serbian Cinderella, or Peruvian Cinderella and check out what comes up. There are lots of opportunities to compare and contrast these well-known stories.

I was thinking you might be able to compare the treatment of women in "The Son's Veto" by Thomas Hardy (English) and "The Story of an Hour" by Kate Chopin (American). Both are available online (see links below). "Veto" is written by a man, and "Story" by a woman, but both authors seem sympathetic to the plight of the female protagonist in both stories—oppressed in a male-dominated society.

"The Son's Veto" - http://www.readbookonline.net/readOnLine/9677/

"The Story of an Hour" - http://www.vcu.edu/engweb/webtexts/hour/

"The Feather Pillow" is a modern Gothic short story by Horacio Quirago, an Argentine author, which you could compare with Hawthorne's "The Birth Mark." Both include the death of a beloved wife and share the primary elements of Gothic literature.

You might also consider comparing Roald Dahl's "Poison"--a short story set in India--with an O. Henry story. Both authors rely heavily on surprise endings, dark irony, and appearance versus reality. O.Henry's "The Furnished Room" is a brief story that might work with "Poison."

I think that many of Edgar Allen Poe’s stories can be contrasted with some Victorian short stories.  For example, Charles Dickens wrote a number of gothic and somewhat creepy short stories that compare well with much of Poe’s gothic, creepiness.  The themes, such as greed, revenge, ambition, and self-loathing are common. 

"The Secret Life of Walter Mitty" by James Thurber compares well with the New Zealand writer Maurice Gee's story,"A Glorious Morning, Comrade".

The character of Walter Mitty, who escapes into fantasy to escape his personal weaknesses and the tyrannical dominance of his wife, compares well to the main protagonist of Gee's story, Mr Pitt-Rimmer. Pitt Rimmer has been a respected member of the legal profession but is now in decline due to Alzheimer's. He sets out to beat his record of escaping fromthe smothering clutches of his daughters.

"An Occurance at Owl Creek Bridge" is an American short story exploring narrative perspective with some dramatic and action elements included. This story could compare to a number of short stories from non-American writers. 

I would look at James Joyce, Franz Kafka and Luis Borges for writers from another culture. You might also look at the work of Oscar Wilde if nothing pops up with the first three writers. 

The protagonists in "Bartleby the Scrivener" by Herman Melville "Metamorphosis" by Franz Kafka could easily be compared and contrasted.  While both protagonists lead monotonous lives, Bartleby's passive defiance of with the words "I would prefer not to" demonstrates refusal to contribute to be a part of his community.  Bartleby chooses not to work and shows no sympathy for his employer or his fellow workers who must take over his duties.

On the other hand, Gregor, the protagonist in "Metamorphosis", does care and does want to be a part of his community. When he realizes he is unable to get up for work, Gregor's mind races. Seemingly unconcerned about becoming an insect, Gregor worries endlessly about being late for work. When he can't, his family complains, neglects him, and his sister ultimately sending him away when he ventured from his room one night to listen to his sister play her violin.  The refusal of the family to include him suggests that this is what ultimately causes Gregor's death.