Claimed by Scott Gingold

We still don't know the details of how claiming works and its relation to the "sickness" and the smoke monster, but we have had clues to its existence early on.

Claire was not claimed during the attack on the barracks by Keamy's men. She was claimed much earlier than that. In fact it happened when she was kidnapped by Ethan. When Boone & Locke found her in the jungle her memory was gone (just like Ben's memory loss after being healed at the temple). Also in "Maternity Leave" we see Ethan giving Claire and in utero Aaron injections from the mysterious vaccine, which may have been to control the "sickness" that she already had. Claire had quite a personality change after the kidnapping. She was very hostile towards Charlie (even before the baby napping incident) and its very possible she had a "growing darkness" inside her, that didn't come out fully until the attack on the barracks.

Ethan and Goodwin were cast out of the Others by Ben. Why would Ben get rid of his only surgeon when he KNEW he had a spinal tumor? Because Ethan & Goodwin had been claimed. In "Maternity Leave" it's implied that Ethan was acting alone on bringing Claire to the Staff station and that the Others did not approve. And Ethan seemed overtly eeeevil, even hanging Charlie from a tree and snapping poor Scott's neck - or was it Steve:) Goodwin wasn't the nicest guy around either. He was cheating on his wife, he sorta jokingly threatened to use the tempest gas to kill everybody, and he broke Nathan's neck. In fact, Goodwin and Ethan were the only Others in seasons 1 & 2 who we've seen kill anybody.

Until Season 3....
Juliet. Juliet killed Danny Pickett. Then she was branded. Branded just as Claire and Sayid were branded. Except Juliet got the neat little tramp stamp. Juliet was also cast out of the Others, because she was no longer worthy. She had been claimed. There's a lot more to Juliet that we haven't seen, especially when she first told Sayid & Sawyer that if she were completely honest with them, they'd kill her. It's also worth mentioning that it was Juliet's idea for Richard to bring Ben to the temple to get healed and it was Juliet who brought Ethan into this world when it seamed like Ethan was destined not to be born (there were complications, it wasn't supposed to happen).

Mikhail. He's killed the most people out of the Others. Bea Klugh, Bonnie, Greta, Charlie, not to mention he shot Sayid. And he kept seemingly coming back to life. The island (cough, cough, the smoke monster) would not let him die.

Ben. Richard brought him to the temple to be healed, but it was already too late. He drowned him in the waters, he was healed and reborn as Benjamin Linus, the King of Cons. But he had already been claimed. In fact he was claimed early on, when following his dead mother through the jungle. But it took Sayid shooting him to act as the catalyst for the change. And Ben became corrupted by the darkness.

Sayid. It seems as if Sayid shooting Ben led to Ben becoming evil Ben, the same evil Ben who groomed Sayid to become the killer who would time travel and shoot young Ben, thus completing the cycle. But Sayid was claimed early on ... before he got to the island. In "One of Them" Inman gives Sayid a choice and it making that choice, Sayid becomes a torturer. It was this decision that tipped the scale of light and darkness within Sayid.

And it's this factor that is what the claiming is. It's a choice. The smoke monster (just like Jacob) believes in free will. Everyone has a choice. Just like Smokey told Sawyer he had 3 choices on what to do next. But it's when one of the characters makes a conscious choice to let in the darkness inside them and do something wrong, that he or she is claimed.

This has been most evident when Michael shot Ana Lucia & Libby. Soon after Michael was manipulated and then not allowed to die. Not by the island, per se, but by Smokey, who now controls him and wouldn't let Michael stop being useful until he really had no more use for him.

Which brings me to Danielle. Charles ordered Ben & Ethan to kill Danielle. Ben couldn't do it, because maybe the darkness hadn't completely corrupted him yet. But why would Charles want to kill Danielle? Because she had been claimed. She behaves just as we've seen Claire behave. She killed her entire crew after they had been claimed. Charles was afraid she would corrupt everyone else on the island. So he ordered her death. And then Ben goes and brings Alex into their midst. So it should have been no surprise that Charles wanted Ben to kill Alex as well. Because Alex had most likely been claimed as well. But since the Others believe in free will and choice, and Ben made the choice to keep Alex around, Charles had to let him. But he let Ben know that if the island wanted Alex dead, she'd be dead.