There are a number of items that may be considered symbolic in William Faulkner's "A Rose For Emily."
The first is the "rose" mentioned in the title. Michael Ferber in A Dictionary of Literary Symbols writes:
Almost any flower can represent a girl, but the rose has always stood for the most beautiful, the most beloved.
There is also the reference, noted by Ferber, that the rose is something with a short life, but the rose is also something that has thorns. Emily Grierson is a rose: for a time she may have felt greatly loved by Homer Baron (or perceived his attentions as such); the relationship between the two was short-lived—and Emily's chance at love dies quickly; and, without a doubt, by the story's end, we know that Emily had "thorns."
In some ways, Emily may symbolize an old way of life. When her father was alive, she was the picture of propriety. When he died, Colonel Sartoris, in the manner of an old Southern gentleman (coming to the aid of a "defenseless young woman") deferred her taxes for the remainder of her life. However, she became more independent: for example, she does not live with another woman in the house, and goes out riding unchaperoned with Homer—she may well represent the decline of the South over time.
Emily is referred to as a "fallen monument." This might refer to the fact that she was once symbolic of the upper-crust of society and has fallen on hard times, lacking a means of support. Her house is old and falling apart—it has seen better days, as has Emily. So while she may have been put on a pedestal by some, those days are gone. However, there is also the sense that "fallen" could symbolize her sexual relationship with Homer, as unmarried women who engaged in sex before marriage were called "fallen" women.
There are numerous references to dust. When the representatives of the community come to her home to collect Miss Emily's taxes, the house smells old, and as they sit, the dust begins to move around them.
It smelled of dust and disuse—a close dank smell...and when they sat down, a faint dust rose sluggishly about their thighs...
The dust may symbolize death, and may even then foreshadow the discovery of Homer's body later in the story.
The breaking of the door seemed to fill this room with pervading dust...A thin acrid pall as of the tomb seemed to lie everywhere...Among [the man's toilet things] lay collar and tie...which, lifted, left upon the surface a pale crescent in the dust.
Looking at the body, having rested in the bed so long, Faulkner describes the dust again:
...upon him and upon the pillow beside him lay that even coating of the patient and biding dust.
It is interesting to remember what is often said at funerals—"ashes to ashes, dust to dust" which...
...is based on scriptural [text] such as "Dust thou art, and unto dust thou shalt return" (Genesis 3:19).
Smell is mentioned several times. It also seems to by symbolic of death and/or decay. When the men visit the house at the beginning of the story (to collect taxes), the house smells—"of dust and disuse"—like a tomb. Later in the story there is the incident of the terrible smell coming from Miss Emily's home: we later learn that it was a dead body. Finally, at the end of the story, the "bridal room" smells:
...and leaning forward, that faint and invisible dust dry and acrid in the nostrils...
Ferber, Michael. A Dictionary of Literary Symbols. New York: Cambridge University Press, 1999.