DESIRES

The starting point of all achievement is desire. Keep this constantly in mind. Weak desires bring weak results, just as a small fire makes a small amount of heat. — Napoleon Hill

Many characters had strong feelings of wanting to have something or wishing for something to happen. Ben informed Locke that the Island was a metaphoric "magic box" where wishes could be granted. In Locke's mind, he wanted to have a showdown with his father. He believed the island granted him that wish.

But desires can also include emotional feelings, sexual wants or an acceptance to belonging to someone else. Kate had numerous sexual relationships during the series but was left with an unfulfilled desire for lasting happiness.

Desire could also be the quest for status or achievement. Charlie always wished to be a rock star, and for one fleeting year he lived his dream. But that dream collapsed quickly under the trappings of stardom. On the opposite end, Hurley tried to run away from his fame and fortune.

Maybe opposites do attract like magnets.  Charlie wanted the fame and fortune but Hurley despised it. On the island, they became good friends.  Kate was always looking to run away from her problems while Jack ran head first into problems in order to solve them. The same could be true with Sawyer and Juliet. Even people in a close relationship had polar opposite beliefs. Rose was a realist on her cancer fate, while Bernard was a dreamer looking for a medical miracle in any corner of the planet. Sayid did the dangerous, hard, dirty work while Shannon was the rich girl who would not lift a finger to help another person.

Some people believe the whole story was just about the main characters finding their "soul mates."
This generalization has too many exceptions. Rose and Bernard were already soul mates before coming to the island. Locke and Boone never found their soul mates because they were alone in the end church. 

Was the final bonding moment commonality? The reason Charlie gravitated towards Claire and her baby was that Charlie was alone in the world. He wanted to have a family, his own family. But his drug addiction and fleeting fame made it impossible for him to correct his path. Claire was also on a downward path. Her car accident destroyed her family relationships with her mother and sister. Her boyfriend dumped her. She wanted to have her own stable family life, but thought she could not do it alone. 

The one common trait Hurley and Libby had was that they were both institutionalized at a mental hospital. It was strange that Hurley never recognized Libby from their time together in the same day room at Santa Rosa when the Tailies were reunited with the beach survivors. And we really have no motivations or desires from Libby that matches what Hurley was thinking or feeling about his life.

Then again, one would be hard pressed to find anything in common between Jack and Kate or Sawyer and Juliet.  Medical professionals whose oath is to do no harm are matched in the after life with murderous criminals. Were Kate and Sawyer the best Jack and Juliet could do?

Maybe a closer analogy is that the island's wishing well was more like an internet dating/match site. There may be some good matches, but most of the output data is just random pairings.