Without changing physically, Harley's character varies depending on the writer. Many people were turned off by the animated version and never gave her a chance afterwords. What they have missed out on is an in-depth character with more to her than "Mistah J" and "puddin."
 
1. Animated TV Show Harley - "Mistah J!" "Puddin'!" Here we have the original intended to purely be Joker's sidekick who brings out a side of the Joker we had never seen prior to her existence. She's fun-loving, goofy and crazy and gained popularity because that is a good combination for a cartoon character.
 
2. Kesel's Harley - Jump ahead 2 years to her very own 2000 solo series! Karl Kesel stayed true to the core character and wrote a ridiculously weird 25 comics about Harley 
going solo with her own group of henchmen. Well, at the time it was relatively successful , but the character was no longer dependent on the Joker. She relied on causing mild scenes in Gotham and relationships/socializing with other people.
 
3. AJ Lieberman's Harley - When Kesel was done, Lieberman wrote #26-38 of her solo series. Many people HATED or ignored these issues because she was written similarly to Catwoman or a sadistic Batgirl. The jokes are few and far between and she is ruthless and murderous and relies on no one. The soft side is there, but the comic relief is mostly gone and is the polar opposite of Harley #1 and 2. She is constantly stealing while being conflicted about love and doing the right thing morally.
 
4. Arkham Asylum/Suicide Squad Harley - Not sure on this yet, but the pictures lead me to believe she had drastically changed again. For the better or worse, who knows? She hasn't shown much personality yet, but I'm seeing little similarities between this one and any of the previous three.
 
If I had to chose I would take #3. How about you?

#1 it was closest to her creators vision of her

#1 it was closest to her creators vision of her

I'll always enjoy classic Harley. She made cartoons epic to watch, and her costume was briliant. GCS Harley was great, and had some really lol-able lines. I'm curious to see how #4 Harls will turn out

Number 1, without a doubt. And Gotham City Sirens. :)

#1 with a bullet fired from a comical oversized popgun.

arkham assylum !!!  

The arkham asylum vision is still by the same creator. It's certainly not the same as the Suicide Squad version either. I'm conflicted between the video game version and the original cartoon version.

i'm going to be the outcast and pick three because 
 

The jokes are few and far between and she is ruthless and murderous and relies on no one. The soft side is there, but the comic relief is mostly gone and is the polar opposite of Harley #1 and 2. She is constantly stealing while being conflicted about love and doing the right thing morally

1 + 2

Classic Harley will always reign supreme in my heart of hearts. But I highly disapprove of the Harley x Joker dynamic so I was really a fan of Kessel's and Lieberman's respective runs on her book. She evolved but kept that same classic Harley persona. They removed her from the dependence she had on the Joker and really molded her character, really showing us her potential. 
 
GCS Harley also pleases me for those reasons (although the more recent issues have been a let down in that aspect) but I really feel they downplay her intelligence in the series. Something I always admired about her in her solo series was she maintained the bubbly, goofball persona but you could tell she was intelligent. That balance was excellent. 
 
When it comes to Arkham Asylum, I wasn't ok with it at first because I was extremely against such a drastic change with her. But I was able to see the joke in the nurses outfit during the Arkham take-over, so I eased into it. With Suicide Squad/Arkham City I'm not sure I'm going to be able to do that. A lot of what makes her character lovable is the balance between the bubbly, funny, cute blonde and the psychotic, ass kicking, murderous woman. A lot of what I'm seeing coming from those two universes is something a bit too dark and brooding for Harley.