I loved this question! If you are writing an essay on this matter, however, be aware of the use of the word "crazy" if you are going to include it in your narrative. In this day and age everything has a politically-correct terminology...DSM IV can definitely help you find her an accurate diagnosis ;) .
But: To answer your question directly- In the years I've taught this story, I have not been able to come to terms with Emily being "crazy."
She is the Faulkner ideal persona of the Old South, itself: The hard-headed, norm-oriented, value-based, old school-ridden individual with a natural inability to accept what has happened: Change.
Surely, the consequences of her thoughts are irrational, criminal, and lead us all to do deem her as "crazy". Yet, if you look at the rationale behind her actions, her "craziness" can actually be labeled under "post traumatic stress" if you want to be real anal about it; the trauma of losing her father, and seeing the world (as she knows it) fade away steadily and leaving her with nothing, and nobody, as support systems.
Concisely- Emily is a traumatized human being who, in her natural state, was borne and raised to be head-strong, value-based, and co-dependent. There is nothing terminally "crazy" about a human being who acts (even if irrationally) in defense of what he or she was made to believe to be reality.
Of course, normal behavior does not include poisoning one's lover and then sleeping in the bed with his corpse. Thus, it is apparent that "Rose for Emily" is a gothic tale. And, while she is a victimizer in her dealings with Homer Barron, Emily is clearly a victim of the repression of the old patriarchal environment in which her father dominates her; so, there is more to her character than merely being "crazy." For, such a repressive life brings about aberrant behavior as one may seek to maintain some personal power against of his/her situation.
It is this struggle to maintain personal power is exactly what motivates Emily. Having lost her family, friends, and way of life of the Old South, Emily cannot accept any more loss. Consequently, she retains her final illusion by not releasing Homer to the modern world in which she is an anachronism.
That Emily has detained her old world in her ancient house is evidenced in final passages of the story:
She died in one of the downstairs rooms, in a heavy walnut bed with a curtain, her gray head propped on a pillow yellow and moldy with age and lack of sunlight....[in another room] The man himself lay in the bed...The body had apparently once lain in the attitude of an embrace, but now the long sleep that outlasts love...had cuckolded him.