If someone is supercilious, he or she is arrogant. You could use the term stuck up
. A person who has an exaggerated self-opinion (someone who thinks he's a lot better than anyone else thinks he is) can also be described as supercilious
This word is used frequently in literature.
From Oscar Wilde's The Picture of Dorian Gray:
"I am told, on excellent authority, that her father keeps an American dry-goods store," said Sir Thomas Burdon, looking supercilious.
From The Mayor of Casterbridge, by Thomas Hardy:
The hay-trusser, which he obviously was, nodded with some superciliousness. Looking towards the village, he continued, "There is something going on here, however, is there not?"
From Babbit, by Sinclair Lewis:
Now they were men and women of the world, very supercilious men and women; the boys condescended to Babbitt, they wore evening-clothes, and with hauteur they accepted cigarettes from silver cases.
And from Theodore Dreiser's Sister Carrie:
There was nothing bold in her manner. Life had not taught her domination — superciliousness of grace, which is the lordly power of some women. Her longing for consideration was not sufficiently powerful to move her to demand it. Even now she lacked self-assurance, but there was that in what she had already experienced which left her a little less than timid.