The Lucky Charm is made by Kairi before her departure from the Destiny Islands. It seems to resemble Sora: the face has spikes similar to that of Sora's hair and it has a crown connecting the charm.
Kingdom Hearts
The charm is made of seashells (precisely, thalassa shells) that provide good luck for travelers. In Kingdom Hearts Final Mix, Sora gets a glimpse of the lucky charm while he is still on the Destiny Islands, while he, Riku and Kairi are gathering provisions for the raft.
After Sora rescues Kairi from Hollow Bastion, she gives it to him for luck and makes him promise to return it to her once he gets things settled, which he promises to do. When he, Donald and Goofy enter the End of the World, Sora takes a look at Kairi's lucky charm, remembering his promise to return it to her.
Kingdom Hearts: Chain of Memories
In Kingdom Hearts: Chain of Memories, the charm is changed into a lucky charm resembling a Paopu Fruit under the influence of Naminé's ability to alter Sora's memories. Although it changes appearance and Sora thought Naminé was the one who gave it to him, he still protects the charm when Larxene grabbed it from him and threatens to destroy it.
Through Naminé's powers, a World Card for Destiny Islands is changed to resemble the fake lucky charm that Sora's was turned into. It was then given to the Riku Replica. This causes "Riku" and Sora to question the validity of the charms and their memories. After another fight with the Replica, the charm turns back into the World Card. Donald and Goofy begin to question the exact relationship Sora and Naminé might have, which causes Sora to leave them behind.
Sora's charm changes back to its original form once Sora remembers Kairi. Towards the end of the game, Sora looks at it to remember Kairi's name, when Naminé tells him that she is "the light in his darkness".
Kingdom Hearts 358/2 Days
In 358/2 Days, Xion collects a few seashells that resemble thalassa shells. She even gives one of them to Roxas while he slept in correspondence to Naminé putting Sora to sleep to begin his memory restoration. When Xion has her nightmare that takes place at Destiny Islands, Roxas appeared in the dream and picked up a thalassa shell while whispering her name. And after Xion faded back to Sora, the only thing left of her was a thalassa shell.
Kingdom Hearts II
In the prologue of Kingdom Hearts II, Kairi is seen threading the lucky charm and contemplating it on the sands of the Destiny Islands, leaving one lone shell to be washed away by the water. Right before the ending credits of Kingdom Hearts II, Sora returns home and finally returns the lucky charm to Kairi.
The lucky charm is also the Keychain for Oathkeeper.
Kingdom Hearts Birth by Sleep
In a a recent trailer, Aqua is shown giving two similar good luck charms to both Ven and Terra, and wears one herself. She states that the Skin of a Paopu Fruit is used to create them and that those who bear them will always return to each other no matter how far apart they are.
Whether that has any connection to Kairi's lucky charm with Sora is yet to be known.
In Deep Space, Stitch seems to have made one based off of Aqua's out of what appears to be space junk.