Harley's origin was, for years, identical in the comics to the one seen in the Batman animated series.
But, in the comic series Harley Quinn, a quite different one was established.
Born Harleen Quinzel, Harley's mother is a somewhat harsh, but forgiving lady, who constantly calls Harley evil and compares her to other heroes. Harley's younger brother is a dead beat with children from at least two different women and still lives in his mothers house. Harley apparently sent him several large sums of money to get his life on track, but he squandered it. Harley's father is a criminal con-man, known for swindling women out of their money with his charm. Harley states that the main reason she became a psychiatrist was so she could understand why her father did what he did to their family.
Harley went to study psychology, but found doing so dull. She tricked her way in to a college.
She came up with a theory about being in love having similarities with being a criminal. About, how far can someone go for love and decided to use her boyfriend, Guy, as the test subject, pretending that she had committed various crimes, such as murdering a teacher, to Guy's surprise. Thinking he was looking out for Harley he shoots an innocent man believing him to be "murdered" professor who hadn't died yet.
Guy thinks that he can`t live with the guilt, and wants to die, but can't bring himself to suicide and asks Harley to kill him instead. And she does, for love, disguising the murder as a suicide.
Traumatized by these events, she begins to believe that universe is in a constant state of chaos, like Guy thought. She represses her feelings of sorrow, and feels connected with the Joker, who believes in some of the same things as Guy, and so finds a job at Arkham Asylum, demanding to speak to him.
During the very first session, she shows the Joker her blossoming insanity, and obsession towards him. Joker finds this appealing, and Harley helps him escape various times, before eventually becoming his henchgirl.
Eventually Harley was caught by Batman and put into a cell in Arkham - she is able to escape time and time again. During the events of No Man's Land she is finally able to escape, immediately choosing to rejoin with the Joker and help him in his crimes. Later, in another retelling of her origin it is explained that she was a psychology student working part time as a stripper to pay her bills.
She lies about Joker having seduced her, and making her gradually insane, later on.
DC's Animated Universe
Harley’s origin was told in Batman: The Animated Series episode and comic entitled Mad Love. The story starts off with Dr. Harleen Quinzel working as an intern in Arkham Asylum. She discovered the Joker and quickly became fascinated with his insane motives. She voluntarily asked for a chance to analyse him. During one of their sessions the Joker tells her about his tragic past and how his father abused him. She gained sympathy for him and quickly fell in love with him. She helped the Joker escape dressed up a the Harley Quinn. So, started her career as the Joker's sidekick.
Later, Harley finds out that everything the Joker had told her was most likely a lie or scam. He was deliberately telling her what she wanted to hear to endear himself to her. This is something that Joker does to Harley all throughout their relationship. She knows this and continually tries to leave him but like an abused spouse, she just keeps forgiving him and runs back into his arms all the time. Of course Harley gets her license revoked when her superior Joan Leland finds out she is the one who released the Joker.
Ever since the beginning of her relationship with the Joker, Harley has played a very submissive role. She has often been used and abused by the Joker to the point where her life has been threatened on several occasions. Yet she remains faithful to her man and stands by him when things go wrong. Quinn's relationship with the Joker is one of the most complex and twisted love affairs in comics. As with all people, Joker is abusive and manipulative towards Harley, but just as often there's evidence of camaraderie, playfulness, and affection towards her. She's the only person who's managed to become intimate on such a long term basis with the Joker and, while he generally accepts their relationship, we even see the Joker's occasional moments of confusion and discomfort which results in attempts to kill her.
Character Evolution
Harley's career as the Joker's sidekick consisted mostly of her being where he could not. He used her less recognizable face to get into places he could not so he wouldn't get arrested, and she was also usually a sort of field leader to Joker's henchmen when Joker himself decided to sit out on whatever they where doing. She was trusted with the intimate details of most of his plans, and as stated earlier, was also often betrayed by Joker when he needed a scapegoat. After a while Harley got fed up with Joker and set off on her own. She even started a gang of her own that didn't last very long due to many or all of the gang being killed shortly after it was formed. She also teamed up with Poison Ivy and had some run-ins with Thorn and Superman.
With the changes brought to the DC Universe by the launch of The New 52 following the events of Flashpoint, Harley has undergone further evolution, with a new look, origin and history. The architect of her changes being Adam Glass. The arc introducing set to introduce the new origin of Harley Quinn, which, according to the series' writer, is set to have a deeper psychological aspect to it, not necessarily changing familiar traits of the character, but adding more to her mythos. Glass has also expressed his belief in Harley being more than just a support character. "I think the difference between the Harley in my book and what Paul Dini did is that I’m writing a Harley that is not about the Joker. Now I’ll go on record for saying this, but I think that Harley Quinn will always be loyal and faithful to the Joker when he is around. But when the Joker is not around she’s a young woman who is very capable of doing many things, and she is her own person."
She appears in the ongoing series titled "Suicide Squad" along side of Deadshot, El Diablo, Black Spider, King Shark, and Sportsmaster. Most notable changes has happened to her wardrobe and general design, with the color scheme of blue and red replacing the most well known black and red combo. Her hair is now exposed, and changed to a half red and blue color, replacing the blonde. Overall her design has been heavily criticized for lacking familiar elements of the quirky clown, sacrificing her usual character qualities for sex appeal. The main issue with the new look is mostly agreed to be lack of jester appearance, which has initially been Harley Quinn's namesake. The only justification to the change from Bruce Timm's classic design given has been that "People liked her look in Arkham Asylum". No real further comment was provided.
Harley's origin was tweaked. She remained a doctor at Arkham Asylum where she "treated" the Joker, but knew from the get go that he was lying to her. Regardless, she still fell for him, and when she found out that her superior was stealing her research for a book, it drove Harley to help the Joker escape. Joker would bring her to the chemical plant where Batman caused the accident that bleached his skin, deforming him, and throws Harley into the same chemicals, causing a similar effect on her.