William Faulkner's "A Rose for Miss Emily" depicts madness in many forms and through many characters.
Miss Emily's father demonstrates a kind of madness when he refuses all of his daughter's suitors because they were not good enough; clearly he was stuck in some notion of the past and could not be realistic about the present.
Homer Barron must have been a bit mad to keep coming back to Miss Emily; he had many indications that he should have left and did not do so.
The town authorities clearly display a kind of madness when they are so thoroughly intimidated by Miss Emily that four grown men slink around her house after midnight, sniffing the ground and spreading lime, hoping Miss Emily will not catch them. Or when they allow her not to pay taxes like everyone else just because she looks at them imperiously and says she will not do so.
Obviously there is plenty of madness to go around in this story, but of course Miss Emily displays the most madness. She keeps her father's dead body for three days before the authorities can finally take it from her. After she and Homer Barron scandalously become lovers, the ladies in town force the Baptist minister to go and talk to her; he never reveals what happened during that interview, but it had to have been outrageously mad since he refused to enter Miss Emily's house again--ever. Her three cousins have the same kind of reaction when they come to chide her for her scandalous behavior. They do not stay long.
Miss Emily certainly displays a kind of madness when she boldly purchases poison and lies about why she needs it; and when she keeps her dead lover's body for years and then sleeps next to him (at least sometimes), she must also have been mad.
Some of what what I am calling madness may just be the quirkiness of an aging Southern belle (a kind of relic) who has been robbed of an opportunity for happiness and therefore prefers her own company to others'; however, Miss Emily also certainly demonstrates madness in some of its most gruesome forms. While it is easy to point to the grotesque and macabre things Miss Emily does, she does many other things worthy of the term "madness."