My take for what it's worth, and take it with a grain of salt if you wish...
as for her early surge in popularity
1) she started out on television so she reached a much larger audience and potential fanbase than a character originating in comics would
2) her origin has a touch of tragedy in it that appeals to said audiences
3A) she has ties to the Joker, perhaps the most iconic and popular super-villain in comic-related pop-culture
3B) she has ties to Batman, the most iconic and popular super-hero figure in comic related pop culture
4) she was actually funny in the animated series, and well written by Paul Dini and his crew, and the humor worked in the context of the show making the character stand out, her voice was distinctive (thanks to the voice actor who played her) and she had a couple of catchphrases that were easily identifiable with the character (Puddin' and Mr. J come to mind)all helping form an iconic presentation that would stick with audiences to create fans
5) her early appearances in comics were few and far between leaving the audience wanting more and not being over-saturated and tired of her off the bat
6) said appearances appeared in books with smaller print runs (the animated tie in books) than the regular line of comics, so the early demand made those books hard to find and garnered some attention in the collectible side of the the hobby as well as the readership side
7) those early appearances were in the same vein and tone as the animated series making them a fun reading experience
8) her 1st costume was iconic and recognizable beyond just the character herself, tapping into an archetype that people could recognize and latch onto with an immediate sense of familiarity, combined with the recognizable identity in the portrayal of the character on screen, this made a powerful foundation to build character popularity on, add in the other factors and you have a good recipe for a successful character...
the second wave of popularity factors seems to be based on less savory (to me) aspects...
1) her transition into a video game character again reached a wider audience than comics
2) her character in the games was often violent to an extreme mixed with the comedy making it darkly (sometime sickly) humorous
3) her appearances/costume was changed to play up the cheesecake factors and appeal to the same adolescent male mentality that dug the dark violent and humor of the video games
4) snark-the later portrayals took the sweet if disturbing humorous aspects of the character and pushed them into the realm of pure snark at the conventions of the hobby and pop culture (much the way Deadpool does) which basically aims for the low hanging fruit to get the laughs with lowest common denominator humor
all the second section informed her movie appearances and the new52 versions as well. So the second wave took the solid foundation of the initial character portrayal, basically a lovable tragic jester who strikes the funny bone and turned it into a darker, sexier and more violent portrayal that cashed in on the core adolescent-level male mentality that dominates a lot of the hobby.
-M
