Background/History:
Like Spike Spiegel, Faye Valentine is a person without a past. However, unlike Spike, who simply doesn't talk about his past, Faye has no idea what her past is. Her earliest memories are being awakened from cold sleep three years ago and of being told she'd been frozen for over fifty years after a serious accident of some sort. Promptly saddled with an enormous debt (300,028,000 woolongs to be exact), Faye fled and has been on the run ever since.

In the course of the show, Faye's memory comes back to her and she remembers who she is (or more accurately -- was). Born in 1994, an orbital shuttle accident in 2014 resulted in Faye being placed in cold sleep. She was unthawed in 2068, her injuries fully healed, but her memories totally gone. Dr. Bacchus, the man who brought her back, named her Valentine, and in an attempt to bilk her for all he could get saddled her with the 300 million woolong debt.

Although Faye first encounters Jet and Spike in Episode 3 Honkey Tonk Women, she doesn't actually join the crew of the Bebop until Episode 4 Gateway Shuffle. She leaves the Bebop (along with Ed and Ein) in Episode 24 Hard Luck Woman, after finding where her home used to be. She rejoins the Bebop in Episode 25 The Real Folk Blues Part 1 after encountering Julia and being given a message to pass along to Spike. At the end of Episode 26 The Real Folk Blues Part 2 she has presumably rejoined Jet on the Bebop.

Personality/Motivation:
At first glance Faye is a self-centered, greedy, conniving, con-woman. This holds pretty true for the second glance as well. The truth, however, is a bit deeper.

Due to her massive debt and her betrayal at the hands of Dr. Bacchus and Whitney Hagas Matsumoto (Faye's "lawyer" when she woke up), Faye has come to the decision she's better of alone, where she can look out for "number one" (herself). She doesn't want to let herself get close to anyone, fearing further heartache and betrayal. In Episode 12 Jupiter Jazz Part 1, Faye leaves the Bebop because she fears she's starting to like Jet and Spike as comrades and is afraid they will abandon her (so she abandons them first).

Faye's debt has also led her to try one "get rich quick" scheme after another. In her case, this involves constant trips to the casinos, where her skill at gambling seems to be offset by her constant runs of bad luck. Of course, Faye simply shrugs her shoulders and comes back whenever she has some extra cash to burn.

Faye shows a remarkable turn around at the end of the series. At the end of Episode 24 Hard Luck Woman we see her laying down in what used to be her house, having used a stick to scratch out the approximate location of her old room and bed. In Episode 25 The Real Folk Blues Part 1 she has left Earth and come to Mars, having realized that in her case "you can't go home again." She has also realized that knowing one's past doesn't magically solve anything. As Spike says to her in Episode 15 My Funny Valentine, "No matter the past, you still have a future." Faye realizes this to be true, and decides to make her way in the world once again. She rejoins the Bebop to pass on Julia's message, and practically has a fit when she discovers Spike is going to go and fight Vicious. The reason is simple -- after realizing she can put her past behind her, Spike is going to confront his -- and will almost certainly die in the attempt. The last we see of Faye is her standing in a passageway of the Bebop, her gun in her hand (she's just fired a few shots in the ceiling), watching Spike leave.

Some people may wonder if Faye has fallen for Spike at this point. I don't think so. Although a "sexy" woman in both dress and actions, Faye isn't interested in a romantic relationship with anyone, Spike included. Her emotional reaction is (IMO) due to the reasons I stated above. After Spike has told her "No matter the past, you still have a future." he is going to confront his past and thus end his chances for a future.

Quotes:
"I'm alone. I dont want comrades... and it's worth having any. I end up worrying about things I don't have to..."
"They often say humans cannot live alone... but you can live pretty long by yourself."

Powers/Tactics:
For someone who has spent 54 years in cold sleep, Faye has adapted to the modern world rather well. She is an accomplished monopod pilot, good enough with a gun to shoot another pistol out of a man's hand, and trained in hand-to-hand combat. She is also a capable gambler, skilled in cards and dice, but has a tendency to cheat. She also fairly quick and agile, which comes as a big help in getting out of the trouble she tends to get into.

Appearance:
Faye stands 5'7" with a slender (but well-proportioned) build. She has shoulder-length dark purple hair cut in the "pageboy" style (and held in place with a yellow-orange hair band). Her clothing consists of a pair of bright yellow shorts/hotpants help in place via suspenders, a matching high-collared vest, and a red sweater slung low on her arms and tied at her midriff. Thigh-high hose and low boots complete her outfit. Faye can (and does) wear other outfits, and does seem to have the clothes for any occasion.