"The Yellow Wallpaper" and "A Rose for Emily" would be two great choices. If you could find a third with a woman main character it would add a multiple layer of meaning to your compare/contrast essay. "The Story of an Hour" by Kate Chopin would be stretching it, but it might be argued that the main character was isolated through her loved ones' desire to protect her from the realities of life. Looking at how woman were isolated would make for an interesting essay.
"The Yellow Wallpaper" is the perfect story for isolation that leads to insanity. Also, there is a story by Julio Cortazar entitled "House Taken Over" in which a brother and sister believe that their house is inhabited by spirits that keep taking more rooms from them.
To add to the list of Poe stories, Roderick and Madeline Usher has been isolated too long in that old mansion that now crumbles. Certainly, the narrator who comes to visit is shocked by some of the occurrences.
I think that "A Rose for Emily" is a pretty clear case of a story that embodies this. For her whole life, Emily has been unable to find herself a man. It's partly her fault and partly her father's, but whoever is at fault, the isolation is real. This isolation has, one can argue, driven her insane. At any rate, it has driven her to the point where she is willing to kill Homer Barron and sleep in the same bed as his corpse.
I think you could make a case for the man who murders the old man in Edgar Allen Poe's "The Tell-Tale Heart." The man can't even really explain to the audience why he killed the man, but being left alone with the dismembered body hidden under his floor boards is enough to drive him crazy. As his guilts grows he starts to "hear" the heartbeat of the dead man, and he ultimately confesses his guilt for the crime.
Okay, I'll admit that the first thing to came to my mind is a novel, and not a short story, but since this is the discussion board, I've just got to put a plug in for Steven King's The Shining. There's just no better example if you ask me. Guy moves to a hotel that can "shine" and, due to the isolation, becomes a murderous victim. The book beats the heck out of the movie, actually, so if you associate The Shining with Jack Nicholson, try reading the actual book. I never thought I'd be afraid to walk by a fire extinguisher, ... but after reading The Shining, it's possible! Ha!
Another story (that pales in comparison with the first, but still ...) that would work with the them of isolation leading to insanity would be "To Build a Fire." Or perhaps it would be better to phrase it "isolation leading to panic." Hmmmm, either way, the man in "To Build a Fire" has isolated himself by not paying attention to gut instinct. He dies as a result.
Perhaps I could even make a case for Lord of the Flies, eh? Is it insane enough to worship a rotting pig's head and kill a classmate? Hmmmm, ... maybe!
The first story that comes to mind is "The Yellow Wallpaper" by Charlotte Perkins Gilman. This is the story of a young woman who is taken to a country house to 'recover' from a type of mental breakdown. She is separated from her children and her husband. She is isolated in the upper levels of the house. It is believed that this time alone will aid in her recovery. Eventually she goes mad. She believes a woman is coming out of the wallpaper. This story would make a great addition to your essay.
These are all great suggestions! I also highly recommend "The Yellow Wallpaper", "A Rose for Emily", and "A Tell-Tale Heart". A bit of a more light-hearted and less serious one would be "The Toynbee Convector" by Ray Bradbury. I always felt like Craig Bennet Stiles was isolated and depressed because of all the pressure that was put on him to make a good show.