Alice Liddell is depicted as being an older version of the little girl from Alice's Adventures in Wonderland and Through the Looking-Glass. After the events of those stories, Alice's home burned down, and while she survived, her family did not, and she was forced to listen to her parents' screams as they burned alive. This drove her into insanity, and she was placed in Rutledge's Asylum.
Alice is seen as a strong female character. She easily holds her own in front of danger and never seems to be frightened in the face of madness. She is said to have a hero complex, wanting to constantly help others even if it means that she will suffer in return. She's also persistent. She does not give up in the face of adversity and usually gets what she wants through perseverance.
Alice's biggest weakness is the fact that she is constantly haunted by the fact that she survived the fire that killed her family. Throughout the games, she tries to piece together her broken psyche through her Wonderland which is in fact her imagination. Her Wonderland represents her state of mind and becomes corrupt and weak when she is not well. It also becomes oppressed by the Queen of Hearts who's a rogue element of her own personality. This element tries to invade Alice and take control (the invasion is usually symbolized by pink tentacles which wrap themselves around certain parts of Wonderland).
Alice murders elements of Wonderland without much thought. She doesn't seem phased by the violence that goes on around her which suggests that she is indeed a little mad. Her ruthless determination along with the fact that she can't seem to control when she enters Wonderland proves that Alice is in need of help. Said help seems at first to appear via her shrink, Bumby, who tries to make her forget. This however leads to her creating a sort of destructive train that instead destroys Wonderland. Wonderland is in fact what keeps Alice sane despite the fact that everything in it is insane.
American McGee's Alice
The events of American McGee's Alice depict Alice finally becoming so demented that she descends into Wonderland once again, and since it has always been a metaphor for Alice's own mind, Wonderland is now dark and twisted, with familiar characters become violent psychotic monsters. The Mad Hatter represents the truths Alice is trying to avoid, the Jabberwock represents her survivor's guilt, and the Queen of Hearts herself is a living incarnation of Alice's insanity. Alice, aided by the White Rabbit and the Cheshire Cat, among others, makes her way across Wonderland and defeats the Queen of Hearts, freeing her mind from the grip of madness.
Alice: Madness Returns
In the sequel, Alice: Madness Returns, Alice is living in Victorian London, and while she's now sane, she's not exactly stable. She lives with a number of other "troubled" children in a small home, run by a psychiatrist who believes that the best course of action is to erase the traumatic memories of the fire from Alice's mind completely through hypnosis. Her backstory is changed slightly so that in addition to her mother and father, Alice also lost an older sister, Lizzie, in the blaze. After seeing hallucinations of the Jabberwock, once again representing her survivor's guilt, Alice returns to Wonderland, which initially appears pristine and magical, but quickly decays into its more familiar nightmare shape, representing Alice's mind threatening to slip back into madness. Alice must once again fight against the dark denizens of Wonderland in order to preserve her hard-earned and dangerously fragile grasp on her sanity.
The game focuses around whether Alice killed her family by setting their home on fire. Throughout the game, Alice constantly doubts her sanity, questioning herself and her own motives. This leads to her creating a destructive train in Wonderland that destroys everything on its path. This train is in fact Alice trying to forget and is conducted by her shrink, Bumby. Alice explains to the player how her home's library was a fire waiting to happen and if she did indeed start the fire, it was not her fault. As Alice dives head first into insanity, she manages to save herself and Wonderland by finding sanity in her long forgotten memories.
In Alice: Madness Returns, Alice is given the last name "Liddell." This is not from the original stories or from American McGee's Alice; Alice Liddell was a little girl who befriended Lewis Carroll, and it is widely believed that he based the fictional Alice's personality off of Liddell's.