Belonging as a theme has different implications depending on the age and social demographic of the main characters. Here are some short stories I think exemplify this theme:
A & P by John Updike
Bernice Bobs her Hair by F. Scott Fitzgerald (or any of the "Josephine" stories by Fitzgerald)
I Know What You Need by Stephen King
Anima by M. John Harrison
The Body by Stephen King (film version is Stand by Me)
"Stand By Me"
"The Most Dangerous Game"--a club you don't want to belong to...the main character is invited to hunt humans with the General. When he refuses, the General hunts him. Thriller!
"The Color of Water"
"Home and Away"- stories of belonging among Australians
"When I was a Puerto Rican"- identity and belonging of PRcans in the US
"The Company of Others: Stories of Belonging"- a compilation.
"A tribute to my White Mother, from her Black Son"- James McBride, right here on Enotes
---Those are surprisingly stories closely-knit to belonging to something, or to a group, or a family.
I'm not sure what age level you're looking for, but many Bradbury short stories, including "All Summer in a Day" deal with belonging. Also, Bless Me Ultima, The Adventures of Huckleberry Finn, Their Eyes Were Watching God, A Separate Peace and Frankenstein all include the motif of belonging. For younger readers, Touching Spirit Bear and Warriors Don't Cry.
In terms of the negative things people do in order to belong to a group or the difficulties these people face finding the right fit, there are a number of young adult novels and short stories centered on teens and peer pressure.
"The Bass, the River, and Sheila Mant" - The protagonist sacrifices his love for fishing to impress the elusive Sheila Mant
"Theme for English B" Langston Hughes' narrator discusses the difficulty of being the only black student in his college composition class.
Any novel or short story by Amy Tan, as the majority of her work deals with the struggles of negotiating between two cultural identities - Chinese and American
The Chocolate War by Robert Cormier - Gives a pretty accurate account of high school politics and the pressure to conform.
I hope that helps!
Some of the books that come to mind are books directed at pre-teen and teenage readers, probably because fitting in is such a major preoccupation of those age groups. Stargirl (and other Jerry Spinelli books), The Giver, Harriet the Spy, a lot of Judy Blume books... Adult choices could be Jane Austen's books, Gone with the Wind.....
The idea of belonging is strongly established in The Great Gatsby through Fitzgerald's examination of the social classes that existed in the country in the 1920s (and still do). Gatsby was born into a poor farm family in North Dakota. As a result, he had no social standing. When he met Daisy, who enjoyed family wealth and standing, he was still poor, but the officer's uniform he wore hid his humble background and made him seem socially appropriate to her. After losing her, Gatsby dedicates himself to building a fortune, believing that wealth will provide him entrance into Daisy's world. It does not. Gatsby does not realize that no matter how much money he might acquire, he will never belong to the Buchanans' social class because he was not born into it. His new money will never have the respectability of old money.
Joseph Conrad's "The Secret Sharer" centers around the theme that "meaning depends upon sharing." In this narrative, an inexperienced captain takes the watch upon himself to prove to the crew that he is a good sailor. While he is on watch, the captain who narrates the story discovers a man that resembles himself in an uncanny manner. Against rules, the captain hides this man in his quarters, for he feels the man is his other self. Leggatt, too, senses the affinity: "As if you had expected me," he tells the captain, who feels that Legatt is the "secret sharer of his life."
However, when the captain of the ship from which the "secret sharer" arrives, Legatt and his hostage realize that they must create a plan to achieve freedom for the hostage. Legatt makes it to land.\ and with him go his secrets.
I'd have to go with any novel or short story by Amy Tan which represents themes of acculturation and belonging as part of an immigrant identity. In many of her works, Tan illustrates the immigrant identity as the model for taking action, or acculturating within a foreign society. Her struggle as an immigrant reveals her need to find a voice, and since she lacks a connection to her unfamiliar surroundings, her self-discovery remains painful. These are all immigrant themes of trying to find a sense of self and belonging in a foreign culture.