Door Between Two Worlds by Mr. Echo Better Be Back

This is not a complete theory in itself, merely a few wrinkles added to a number of outstanding theories that lesser mortals like myself could only dream of concocting.

I stand on the shoulders of giants (rather than giant statues!)

If we assume that there are indeed two worlds - parallel worlds -, that fact alone raises a number of questions.

First, how are they related?

We have seen evidence that the two realities are similar yet markedly different. If we are to follow the branching theory of time and space, then logic dictates that at one point in time the two worlds were the same. Some choice or intervening event brought about two separate timelines. Or to think of it in another way - to borrow another poster's analogy - a big rock was dropped in the middle of the stream and now we have two forks.

If we assume that as true, other questions arise. Multi-dimensional theory posits that an infinite number of worlds exist. Why are these two somehow connected? There are a number of reasonable possibilities:

1. The two worlds are on either side of the boulder and only exist separately for as long as the universe takes to course correct and create a single timeline. This possibility is interesting and ties in well with a number of themes mentioned in the show including: the nature of free will vs. destiny, the Dharma initiative trying to alter the Valenzetti equation and avoid the inevitable end of the world, ect.

On a side note, It is entirely possible that the MIB is merely fate personified (the embodiment of course correction) and had to be bottled up on the island so that Jacob, Dharma, Elenoir and others may make permanent their half of the split timeline and avoid course correction.

To accomplish a redirection of the timeline, one would presume to need a device or means of supernatural proportion which would free the actors from the constraints of 3 dimensional existence. If this theory is true, then the island, with its special properties, would be the catalyst for the changes. Supposedly, the island enables time travel which would serve as a useful tool to go back and change things. Perhaps change things over and over a number of times before the desired changes in the timeline are perfected and made permanent. This dynamic is the most popular among theorists.

2. That the two worlds are actually parallel worlds separated by a choice or decision or some other intervening event in the past that tied the two worlds together. For this theory to hold water, the two worlds would need to be tied together so as to allow travel between them. Perhaps the island, with its strange properties, exists in both worlds. In addition, perhaps there is only a single island existing in and bridging two distinct and separate worlds.

The island would then be a door allowing people to travel between parallel dimensions. This would mean that two separate dimensions which should have been forever divorced once created, continually modify each other as people go back and forth. This leads to some exciting possibilities.

This theory would explain why seemingly contradictory events seen in the show could both be true. Some scenes and people we have seen came from one world, some from the other. When the island is moved, it merely bridges the worlds at a different place and possibly another time.

3. A hybrid of the above two theories. The island itself was used to create a second timeline - presumably in an effort to save the world - and so long as the island exists both timelines exist. If the island is destroyed, then presumably the two timelines (or dimensions to maintain continuity with the previous theory) would be forever disconnected. In that sense, to those left in one timeline or the other, the other world would be destroyed.
If your home, the universe you believe is your own, will eventually end in destruction, then preserving the island is absolutely necessary as all hope of modifying your universe rests in being able to time travel, jump universes, ect. On the other hand, if your universe is the happy one not destined for self destruction, then the island represents only danger. The island, and those using it to hop between worlds and times, holds the potential to destroy your world by modifying the good timeline.
This would explain why the island is such a point of conflict. It holds the potential for salvation and destruction.

As to the issue of mental "bleeding" between the two worlds, I believe another’s theory referencing The Dark Tower by Stephen King applies regardless of which of the above theories is true. Since the two worlds are connected, and the islands properties serving as the tether, those exposed to the island's electromagnetic anomalies are able to mentally connect with their counterpart in the other reality. Eventually, they will remember two lives lived as their minds forge unity. Presumably, all the rules of mind travel and mind unity would not apply to those actually on the island as it is the fulcrum between the two worlds.

Now taking in the above theories, it is possible to postulate a number of new theories. First, there is no right or true world. They both exist and neither is "better" than the other in the grand scheme of things.

What compels Desmond, Charlie, Daniel, and others to want to connect to the new world is not a sense of wrongness with their life or their universe, but rather, that the proverbial grass (for them at least) is greener on the other side. The show isn't about love in a universal "love conquers all" sense, or in the sense that love binds cosmos together. But rather, these three relatively lonely individuals have thrust upon them a deep and compelling, wholly realized, love with a person they have never met. It is this love, and the sudden and abrupt realization of it, that compels them to want to discover their other self; their other life. Desmond's purpose on the island is to protect his world, his life with penny. The other Desmond's purpose is to awaken the other passengers on the plane to the knowledge of loves and experiences that are their own but they have never known.

Phew. Thanks everyone. This was a labor of love (and a bit of boredom at work).