Eddie had some, let's say, troubles with women. Basically everyone he loved was prone to die sooner or later. Do you need any more reasons to drink yourself to death?
As so often in his gothic tales, the two women in this story don't represent unique characters, but rather ideas or concepts. The narrator has to admit he doesn't even know Ligeia's last name. Her first name means 'dark, beautiful voice' in Greek, and that's exactly how he describes her. Although her successor, Rowena, is given a last name by Poe, her Anglo-Saxon first name simply means 'fair-haired' – echoing the only words she is characterized with.
Perhaps not by chance, Ligeia rhymes with idea. She represents wisdom and knowledge, a muse and 'holy mother' for the narrator, while Rowena is pure flesh, a mortal replacement, only achieving Ligeia's spirituality in the moment of death. The origin of this image may be the death of Poe's mother, whom he lost at the age of three to tuberculosis. Some say he was unconsciously trying to find her in every relationship he had thereafter.
Another archetype here is the original sin: We have the beloved wife, the forbidden lore, and the catastrophe. Consider though that no one here eats from the tree of knowledge: Ligeia dies before the narrator can decipher the secret of her dark eyes.
Some more general interpretations see Ligeia as a rebirth metaphor, where man's will doesn't die together with the body, but unites with God's will (this is Poe's concept in Eureka). The process of living and dying repeats forever, and Death always shows the same face (hence Rowena's transformation). This interpretation ignores any signs of a violent death in the story, like the red drops of poison in the wine.
Some critics avoid to explicitly refer to Poe's biography in their interpretation and make the tale a study in abnormal psychology. Ligeia becomes an imaginary construct of the narrator, an ideal similar to Poe's. This would explain the lack of proper names. The protagonist murders Rowena while tripping on opium to incarnate his ideal. He then relieves his guilty conscience by making up ghostly apparitions. Against this theory stands the real terror of the narrator when Ligeia returns unexpectedly.
The 'wackiest' interpretations naturally come from the Freud scholars. Every person in the story is assigned to someone in Poe's life. The husband is of course Eddie himself, Ligeia is the phantom mother and Rowena is his child-wife cousin Virginia or possibly his foster mother Frances Allan. Ligeia's eyes become a vagina symbol and her hidden knowledge is that of carnal love. It gets better: The red drops in the wine are the bloody coughs of the mother, dying of consumption.
Murder or reincarnation – it's obvious we'll never be able to completely see into this story, mostly because of Poe's favorite stylistic device, the unreliable narrator. The scrupulous precision of the Ligeia discourse would surely have amused him, being so fond of the enigmatic.
Poe exegesis:
Hoffman, Daniel (1972). Poe Poe Poe Poe Poe Poe Poe. London: Garden City, New York: Double Day.
Wagenknecht, Edgar (1963). Edgar Allan Poe: The Man behind the Legend. New York: Oxford University Press.