The fact that Roderick and Madeline are twins is crucial because it emphasizes the close connection between the Usher siblings. If they were just a regular brother and sister, then it would be more difficult to understand how their fates are inextricably linked. Just as they were raised up together, so too must they fall together. They share a single soul that they also share with the creepy Gothic mansion in which they live. When one of this unholy trinity falls, the other two fall with it, and that's precisely what happens at the end of the story.

In making Roderick and Madeline twins Poe is also tapping into the long-standing cultural prejudice, still current in his day, which held that there was something decidedly unnatural, something inherently dark and malevolent about twins. Twins were often presented in popular literature as being possessed by dark, Satanic forces that made them especially prone to commit unspeakable acts of evil.

Though it's never explicitly spelled out what evil acts, if any, have been committed by the Usher twins, there's no doubt that there's something more than a little unnerving about them, and about the weird connection they share.

Roderick and Madeline Usher came into the world at the same time, and she has been

his sole companion for long years, his last and only relative on earth. "Her decease," he said, with a bitterness which [the narrator] can never forget, "would leave him (him the hopeless and the frail) the last of the ancient race of the Ushers.

Madeline has always been Roderick's companion because they were born together—they even shared a womb—and thus there is a sense that they are much closer than a regular brother and sister would be. Neither would be able to recall life without the other or, possibly, conceive of what life would be like without the other. Further, the narrator says,

A striking similitude between the brother and sister now first arrested my attention; and Usher, divining, perhaps, my thoughts, murmured out some few words from which I learned that the deceased [Madeline] and himself had been twins, and that sympathies of a scarcely intelligible nature had always existed between them.

Thus, Roderick intimates that he and Madeline are close in ways that no one, not even an average brother and sister, could understand because of their relatively unique relationship.

Roderick and Madeleine, as twins, are part of an enigmatic and not entirely understood group of individuals. Twin siblings have demonstrated through research that they share a tremendous psychological connection, and some even dare say that this connection transcends the physical world. 

Evidence of this is found in the story in the words of the narrator:

A striking similitude between the brother and sister now first arrested my attention; and Usher, divining, perhaps, my thoughts, murmured out some few words from which I learned that the deceased and himself had been twins, and that sympathies of a scarcely intelligible nature had always existed between them.

In their case, Roderick can sense the feelings and emotions of Madeline, who is in a catatonic state for reasons that we can only speculate. Yet Roderick feels that Madeline "walks about." Since they are indeed twins it makes it seem almost possible that the two, sharing such a rare genetic uniqueness, are also able to establish communication telepathically.  

Therefore, the twin connection is a clever way to add enigma to the character of Roderick. That the twins are born to a family with a genetic predisposition to self-destruction makes the problem of the story all the more tragic. 

I believe that Poe had the two siblings be twins, rather than just brother and sister, because he wanted to emphasize just how close they were.  People often say that twins are closer than regular siblings because they are the same age and have grown up together from the moment they were conceived.

The siblings' closeness is relevant because of how closely their fates are connected.  They both are seemingly quite ill and eventually, they die at the same moment -- their fates are intertwined.  By writing them as twins, Poe makes it more sensible for them to have such a bond that they would share a tragic fate.

The twin relationship enhances the Gothic effect of the grotesque: Here are a brother and sister who have a bizarre relationship--there blood line is too thin; their being twins thins the line even more. Roderick suffers from a morbid nervous condition while his sister has a strange apathetic illness with catalepsy that keeps Roderick nearby in the mansion that decays as the family does. And, since Madeline is his own flesh and blood, Roderick has the twin intuition that senses what the other feels and thinks. Thus, when Roderick tells the narrator that Madeline still moves in the house and is not dead, there is more credibility given to his declarations. In the final horror, Madeline "bore him to the floor a corpse"; they are united in death and they were in birth--an eerie ending made more plausible because they are twins.

Yes. There are several. First, traditionally twins are often joined or linked in some way. This makes it more likely that they would stay "in contact" after her death. Second, twins are a kind of double; if one is dead, the other is too. Third, this allows them to function as the male and female principle in a psyche, with the house being the larger psyche. That way, their connection is like a link to the subconscious…and maybe madness.

In the 19th century, there was a lot of specualtion about the supposed psychological link between twins, and Poe capitalizes on this in "The Fall of the House of Usher".  The fact that this is the case for Roderick and Madeline adds to the horror when Madeline is buried alive.  The "psychic link" between them is what creates the paranoia in Roderick and the eventual realization about what he did to his sister.  He seems to sense her fears and her anguish, and they are reflected in his behavior.  When she finally does appear outside the door, Roderick is certain that she is there before the door is even opened.  Again, this adds to the horror of the tale.  Having the two die nearly simultaneously reflects the link between twins.

Another interesting, yet morbid and controversial, twist to the twins link is that the Usher family most likely has a history of incest, which means their family has been "inbred" for centuries.  Incest can lead to offspring born with mental illnesses, along with other maladies, so this ties into the twins story well.

Richard and Madeline are a lot like the two halves of the yin-yang: both light and darkness paired in balance with each other. Because they were twins, there was a closer biological and symbolic bond between the two. Just as the house is separating but singular, twins are the same way, reproductively speaking.

A single egg splits, and two entities are formed, much like the splitting or cracking of the Usher house. The metaphor is extended by Poe's choice to make the two characters twins. If they were only brother and sister, the symbolism would not have been as complete.

For a closer identification. To be a twin is to be identical (ideally), and twins share more than other siblings. They share the same womb environment, and, due to being the same age, move through life at the same stages, experiencing the same history. Culturally, there is the association that they share some closer mental or spiritual link. (Think of the movie "Twins" for an example.) This link fits with the sense that they are the same person, or interwoven at a greater than physical level.