I'm looking for interesting literature that characterises people's desire for status/fame/recognition. What are the greatest novels / plays / … on this subject?
The most popular example of fiction characterizing the desire for fame, status, and recognition is The Great Gatsby by F. Scott Fitzgerald.
This novel presents several characters that are fixated on appearances, on the power than wealth brings, and on the special status attached to monetary wealth. Jay Gatsby in particular is associated with ideas of notoriety, glamour and a fixed desire to succeed in the eyes of the world.
His ill-gotten wealth is acquired solely to gain acceptance into the sophisticated, moneyed world of the woman he loves...
Death of a Salesman, the great play by Arthur Miller, takes up the themes you are interested in as well, looking at a man beset by his delusions regarding the importance of being a "success" and being "well-liked".
Through his main character, Willy Loman, Miller examines the myth of the American Dream and the shallow promise of happiness through material wealth.
Another novel that explores similar themes, this time in a business setting, is Babbit by Sinclair Lewis. This novel examines the importance of appearances and conformity to a person's ability to succeed in America.
Other works to consider are The Fountainhead by Ayn Rand and the famous film, Citizen Kane.