Before coming to a conclusion as to what really happened several ideas from the story have to come in to play. When her father died she couldn't accept it and it took several people to convince her that he was dead and to let them bury the body. According to the townspeople he ran off her suitors and robbed her of finding true love and fulfillment. She never seemed able to accept the fact that time was passing and things were changing and maybe this led to her having a fear of being alone. Last but not least she was probably tired of all the town talking about her all the time and may have believed this was her way of solving the talk and being left alone. She did have an image to uphold.
There are several things that point to Emily killing Homer that really can not be ignored. Her going to the store and buying poison but not really giving the pharmacist a reason for needing it so that he writes for rats on the box. Homer entering the house one night after the cousins have left town and never being seen again. Emily tries to get the townspeople to think things are going in the direction they want them to when she goes out and