Necklaces are a form of jewelry that have been used in the storyline of Lost several times by various characters. While several necklaces are symbolic of religion, love, or philosophy, others are simply objects on strings put there for safekeeping and convenience, or purely for decorative purposes.
Necklaces and love
Several necklaces have been worn by characters to symbolize their love for another person. Before coming to the Island, Sun refused a gift of a pearl necklace from Jae Lee, which he gave to her out of his love for her. After Jin beat Jae Lee on Mr. Paik's orders, Jae Lee flung himself from his apartment building window, falling to his death. In his hand was clutched the necklace he had attempted to give Sun, symbolizing that he died for her love. ("The Glass Ballerina")
On Kate's wedding day, Suzanne Callis gave Kate a beautiful locket which she had never been able to give to her daughter because all her children had been male. By giving her the necklace, Suzanne showed her trust in Kate, and her willingness to love her as a daughter that she had never been able to have. ("I Do")
Eko as a young child wore a cross around his neck. When he was taken from his village after shooting a man, Yemi began to wear his brother's necklace to symbolize his Christianity. Yemi was wearing his cross when the Beechcraft crashed on the Island, killing him and the rest of the men on the plane. Eko later discovered Yemi's corpse on the Island, and was able to identify it by the cross. Eko took it for his own again, wearing it for the rest of his time on the Island to show his renewed faith. ("The 23rd Psalm")
Libby wore a stylized silver cross on a silver chain when she met Desmond in the coffee shop ("Live Together, Die Alone, Part 1") and when she talked to Eko in the Sydney Airport ("?"). The necklace was likely lost during or shortly after the crash, as she was not seen wearing it on-Island.
Necklaces for safekeeping
Because Bernard's fingers would always become bloated on planes, Rose would keep his wedding ring on a string around her neck for safekeeping. While sitting on the beach after the crash, Rose would rock back and forth, clutching the ring, waiting for her husband. ("Pilot, Part 2") Rose wore the ring on the string for the majority of season one, until Bernard returned to her at the beach camp, and they tearfully reunited. ("Collision") She then presumably gave him back the ring.
Jack, throughout the first two seasons, wore the key to the Halliburton case around his neck, for safekeeping. The case was full of guns, and in order to keep the guns from falling into the wrong hands, Jack kept the key around his neck. When he first entered the Swan station, the key was drawn up from his chest by an electromagnetic force until it pointed at the wall. ("Man of Science, Man of Faith") Finally, Jack took off the key necklace, ("The Long Con"), and its current owner is unknown.
Upon their arrival on the island, Ben and Roger Linus were greeted by DHARMA workers, and were given leis, decorative necklaces made of colorful flowers, in order to welcome them to the island. The leis were put around their necks by Casey and June. ("The Man Behind the Curtain")
Sawyer and Cassidy, as part of their career as con artists, sold false necklaces for the price of real necklaces in order to earn money. ("The Long Con") Cassidy, after being left by Sawyer, attempted the con by herself, but was almost exposed by two skeptic men. ("Left Behind")
Charlie, on the island, wore a decorative corded necklace with no apparent meaning.
The ankh necklace
Paul has a necklace that resembles the Egyptian ankh symbol. This hieroglyph, which means “life”, was often used to show Pharoahs as having been conferred with life after death. As such, the symbol is often associated with immortality.  Egyptian gods are often depicted as carrying it by its hoop, or holding one in each hand, crossing their chest, similar to the statue of Taweret. ("LaFleur")