Juliet

Pre-Crash: Juliet had been on the island for about three years at the time of the plane crash. Previous to that, she was in Miami working on fertility experiments and was successful in impregnating her ill sister.
She was approached by Dr Alpert to work for Mittelose Bioscience, but she was very sad to say that her ex husband, Edmund Burke, would never let her and the only way would be if he got hit by a bus. Later, Edmund was hit by a bus, most likely as a result of someone at Mittelos, and Dr. Alpert approached Juliet again.
Juliet took the job, despite having to leave her sister behind with no contact for six months.
Juliet couldn't figure out what was wrong with the pregnant women, and they kept dying. She told Ben she thought it was happening at conception and she wanted to take a woman back with her to Miami. Ben said no and she said it was time for her to go home.
Ben told Juliet that her sister's cancer had returned, but that if she stayed and helped them, Jacob would make the cancer go away.
Juliet stayed. Three years later she discovered Ben had cancer and believed he lied to her, but he showed her live footage of her sister playing with her toddler son.
Island: Unlike the rest of the Others, Juliet doesn't seem to bow to Ben's wishes. She knew that Ben had a crush on her. Ben got her lover, Goodwin, who was married, killed. She interacts a lot with Jack while Jack is in captivity in the Hydra. She tells Jack that he can trust her and secretly asks him to let Ben die when Ben is counting on Jack to remove a tumor from his spine.
When Jack tells Tom of Juliet's plan, Juliet denies it. Ben wakes during the surgery and talks to Juliet. She comes out and asks Jack to save him, later telling him that Ben had promised she could go home.
Juliet helps Kate, Sawyer, and Karl escape off the smaller island by shooting Danny Picket.
Juliet claims to have been left behind when the Others left their camp, but it was a plan devised by Ben to get Juliet into the survivors' camp.
Strong Relationships: Jack
Rocky Relationships: Ben. Juliet doesn't seem to like Ben, but it's his decision whether or not she leaves the island.